WorksheetsGeometry Theorem Quiz
Total questions: 113
Worksheet time: 57mins
Name
Class
Date
1.
Segment congruence is reflexive, symmetric, and transitive.Reflexive For any segment AB, AB — ≅ AB — .Symmetric If AB — ≅ CD — , then CD —≅ AB — .Transitive If AB — ≅ CD — and CD —≅ EF — , then AB — ≅ EF — .
a)
2.1 Properties of Segment Congruence
b)
3.2 Alternate Interior Angles Theorem
c)
10.20 Segments of Secants and Tangents Theorem
d)
6.12 Hinge Theorem
2.
Angle congruence is reflexive, symmetric, and transitive.
a)
2.2 Properties of Angle Congruence
b)
6.5 Circumcenter Theorem
c)
8.1 Perimeters of Similar Polygons
d)
3.7 Alternate Exterior Angles Converse
3.
All right angles are congruent
a)
2.3 Right Angles Congruence Theorem
b)
7.20 Kite Opposite Angles Theorem
c)
2.5 Congruent Complements Theorem
d)
8.7 Converse of the Triangle Proportionality Theorem
4.
If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.
a)
2.4 Congruent Supplements Theorem
b)
9.3 Pythagorean Inequalities Theorem
c)
10.14 Tangent and Intersected Chord Theorem
d)
7.3 Parallelogram Opposite Sides Theorem
5.
If two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent.
a)
2.5 Congruent Complements Theorem
b)
6.8 Triangle Midsegment Theorem
c)
7.2 Polygon Exterior Angles Theorem
d)
7.3 Parallelogram Opposite Sides Theorem
6.
Vertical angles are congruent
a)
2.6 Vertical Angles Congruence Theorem
b)
5.5 Side-Angle-Side (SAS) Congruence Theorem
c)
8.6 Triangle Proportionality Theorem
d)
Corollary to the Converse of the Base Angles Theorem
7.
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
a)
3.1 Corresponding Angles Theorem
b)
8.2 Areas of Similar Polygons
c)
9.9 Law of Sines
d)
6.13 Converse of the Hinge Theorem
8.
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
a)
3.2 Alternate Interior Angles Theorem
b)
9.10 Law of Cosines
c)
3.12 Lines Perpendicular to a Transversal Theorem
d)
5.9 Hypotenuse-Leg (HL) Congruence Theorem
9.
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
a)
3.3 Alternate Exterior Angles Theorem
b)
Corollary 7.3 Rectangle Corollary
c)
2.4 Congruent Supplements Theorem
d)
5.1 Triangle Sum Theorem
10.
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
a)
3.4 Consecutive Interior Angles Theorem
b)
6.7 Centroid Theorem
c)
10.12 Inscribed Right Triangle Theorem
d)
2.4 Congruent Supplements Theorem
11.
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
a)
3.5 Corresponding Angles Converse
b)
Corollary to the Converse of the Base Angles Theorem
c)
10.1 Tangent Line to Circle Theorem
d)
7.8 Parallelogram Opposite Angles Converse
12.
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
a)
3.6 Alternate Interior Angles Converse
b)
9.6 Right Triangle Similarity Theorem
c)
10.10 Measure of an Inscribed Angle Theorem
d)
5.7 Converse of the Base Angles Theorem
13.
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
a)
3.7 Alternate Exterior Angles Converse
b)
10.9 Equidistant Chords Theorem
c)
10.20 Segments of Secants and Tangents Theorem
d)
3.12 Lines Perpendicular to a Transversal Theorem
14.
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
a)
3.8 Consecutive Interior Angles Converse
b)
10.14 Tangent and Intersected Chord Theorem
c)
10.17 Circumscribed Angle Theorem
d)
3.12 Lines Perpendicular to a Transversal Theorem
15.
If two lines are parallel to the same line, then they are parallel to each other.
a)
3.9 Transitive Property of Parallel Lines
b)
10.1 Tangent Line to Circle Theorem
c)
10.18 Segments of Chords Theorem
d)
7.17 Isosceles Trapezoid Opposite Angles Theorem
16.
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
a)
3.10 Linear Pair Perpendicular Theorem
b)
6.5 Circumcenter Theorem
c)
3.4 Consecutive Interior Angles Theorem
d)
2.6 Vertical Angles Congruence Theorem
17.
In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
a)
3.11 Perpendicular Transversal Theorem
b)
7.17 Isosceles Trapezoid Opposite Angles Theorem
c)
6.12 Hinge Theorem
d)
6.7 Centroid Theorem
18.
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
a)
3.12 Lines Perpendicular to a Transversal Theorem
b)
6.2 Converse of the Perpendicular Bisector Theorem
c)
4.3 Reflections in Intersecting Lines Theorem
d)
8.8 Three Parallel Lines Theorem
19.
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
a)
3.13 Slopes of Parallel Lines
b)
10.5 Similar Circles Theorem
c)
7.11 Rhombus Diagonals Theorem
d)
8.5 Side-Angle-Side (SAS) Similarity Theorem
20.
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is −1. Horizontal lines are perpendicular to vertical lines.
a)
3.14 Slopes of Perpendicular Lines
b)
9.10 Law of Cosines
c)
9.5 30°-60°-90° Triangle Theorem
d)
Converse of the Angle Bisector Theorem
21.
The composition of two (or more) rigid motions is a rigid motion.
a)
4.1 Composition Theorem
b)
6.7 Centroid Theorem
c)
9.9 Law of Sines
d)
3.14 Slopes of Perpendicular Lines
22.
If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is the same as a translation. If A" is the image of A then1. If AA" is perpendicular to k and m, and2. AA" =2d, where d is the distance between k and m.
a)
4.2 Reflections in Parallel Lines Theorem
b)
10.14 Tangent and Intersected Chord Theorem
c)
10.16 Angles Outside the Circle Theorem
d)
10.6 Congruent Corresponding Chords Theorem
23.
If lines k and m intersect at point P, then a reflection in line k followed by a reflection in line m is the same as a rotation about point P. The angle of rotation is 2x°, where x° is the measure of the acute or right angle formed by lines k and m.
a)
4.3 Reflections in Intersecting Lines Theorem
b)
6.11 Triangle Inequality Theorem
c)
5.8 Side-Side-Side (SSS) Congruence Theorem
d)
8.2 Areas of Similar Polygons
24.
The sum of the measures of the interior angles of a triangle is 180°
a)
5.1 Triangle Sum Theorem
b)
10.9 Equidistant Chords Theorem
c)
8.7 Converse of the Triangle Proportionality Theorem
d)
10.10 Measure of an Inscribed Angle Theorem
25.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
a)
5.2 Exterior Angle Theorem
b)
6.10 Triangle Larger Angle Theorem
c)
6.1 Perpendicular Bisector Theorem
d)
8.5 Side-Angle-Side (SAS) Similarity Theorem
26.
The acute angles of a right triangle are complementary
a)
Corollary to the Triangle Sum Theorem
b)
2.2 Properties of Angle Congruence
c)
3.10 Linear Pair Perpendicular Theorem
d)
7.14 Isosceles Trapezoid Base Angles Theorem
27.
Triangle congruence is reflexive, symmetric, and transitive.
a)
5.3 Properties of Triangle Congruence
b)
10.6 Congruent Corresponding Chords Theorem
c)
8.6 Triangle Proportionality Theorem
d)
10.15 Angles Inside the Circle Theorem
28.
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
a)
5.4 Third Angles Theorem
b)
2.2 Properties of Angle Congruence
c)
3.7 Alternate Exterior Angles Converse
d)
7.18 Trapezoid Midsegment Theorem
29.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
a)
5.5 Side-Angle-Side (SAS) Congruence Theorem
b)
10.14 Tangent and Intersected Chord Theorem
c)
6.8 Triangle Midsegment Theorem
d)
10.7 Perpendicular Chord Bisector Theorem
30.
If two sides of a triangle are congruent, then the angles opposite them are congruent.
a)
5.6 Base Angles Theorem
b)
5.11 Angle-Angle-Side (AAS) Congruence Theorem
c)
7.18 Trapezoid Midsegment Theorem
d)
3.3 Alternate Exterior Angles Theorem
31.
If two angles of a triangle are congruent, then the sides opposite them are congruent.
a)
5.7 Converse of the Base Angles Theorem
b)
Corollary 7.4 Square Corollary
c)
10.2 External Tangent Congruence Theorem
d)
5.4 Third Angles Theorem
32.
If a triangle is equilateral, then it is equiangular
a)
Corollary to the Base Angles Theorem
b)
10.16 Angles Outside the Circle Theorem
c)
9.2 Converse of the Pythagorean Theorem
d)
3.12 Lines Perpendicular to a Transversal Theorem
33.
If a triangle is equiangular, then it is equilateral.
a)
Corollary to the Converse of the Base Angles Theorem
b)
3.4 Consecutive Interior Angles Theorem
c)
10.18 Segments of Chords Theorem
d)
7.13 Rectangle Diagonals Theorem
34.
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
a)
5.8 Side-Side-Side (SSS) Congruence Theorem
b)
2.2 Properties of Angle Congruence
c)
6.13 Converse of the Hinge Theorem
d)
10.13 Inscribed Quadrilateral Theorem
35.
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
a)
5.9 Hypotenuse-Leg (HL) Congruence Theorem
b)
3.2 Alternate Interior Angles Theorem
c)
10.17 Circumscribed Angle Theorem
d)
6.3 Angle Bisector Theorem
36.
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
a)
5.10 Angle-Side-Angle (ASA) Congruence Theorem
b)
8.9 Triangle Angle Bisector Theorem
c)
6.6 Incenter Theorem
d)
6.3 Angle Bisector Theorem
37.
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
a)
5.11 Angle-Angle-Side (AAS) Congruence Theorem
b)
8.8 Three Parallel Lines Theorem
c)
10.10 Measure of an Inscribed Angle Theorem
d)
7.16 Isosceles Trapezoid Diagonals Theorem
38.
In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
a)
6.1 Perpendicular Bisector Theorem
b)
8.9 Triangle Angle Bisector Theorem
c)
9.3 Pythagorean Inequalities Theorem
d)
10.19 Segments of Secants Theorem
39.
In a plane, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.
a)
6.2 Converse of the Perpendicular Bisector Theorem
b)
5.9 Hypotenuse-Leg (HL) Congruence Theorem
c)
3.14 Slopes of Perpendicular Lines
d)
7.4 Parallelogram Opposite Angles Theorem
40.
If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.
a)
6.3 Angle Bisector Theorem
b)
7.11 Rhombus Diagonals Theorem
c)
6.8 Triangle Midsegment Theorem
d)
4.3 Reflections in Intersecting Lines Theorem
41.
If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.
a)
Converse of the Angle Bisector Theorem
b)
3.6 Alternate Interior Angles Converse
c)
3.8 Consecutive Interior Angles Converse
d)
2.4 Congruent Supplements Theorem
42.
The circumcenter of a triangle is equidistant from the vertices of the triangle
a)
6.5 Circumcenter Theorem
b)
6.2 Converse of the Perpendicular Bisector Theorem
c)
Corollary to the Base Angles Theorem
d)
9.2 Converse of the Pythagorean Theorem
43.
The incenter of a triangle is equidistant from the sides of the triangle.
a)
6.6 Incenter Theorem
b)
6.5 Circumcenter Theorem
c)
7.16 Isosceles Trapezoid Diagonals Theorem
d)
9.4 45-45-90 Triangle Theorem
44.
The centroid of a triangle is two-thirds of the distance from each vertex to the midpoint of the opposite side.
a)
6.7 Centroid Theorem
b)
8.4 Side-Side-Side (SSS) Similarity Theorem
c)
3.3 Alternate Exterior Angles Theorem
d)
6.5 Circumcenter Theorem
45.
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.
a)
6.8 Triangle Midsegment Theorem
b)
6.5 Circumcenter Theorem
c)
10.14 Tangent and Intersected Chord Theorem
d)
3.11 Perpendicular Transversal Theorem
46.
If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
a)
6.9 Triangle Longer Side Theorem
b)
2.4 Congruent Supplements Theorem
c)
Converse of the Angle Bisector Theorem
d)
10.18 Segments of Chords Theorem
47.
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
a)
6.10 Triangle Larger Angle Theorem
b)
3.3 Alternate Exterior Angles Theorem
c)
Corollary 7.4 Square Corollary
d)
10.13 Inscribed Quadrilateral Theorem
48.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
a)
6.11 Triangle Inequality Theorem
b)
8.3 Angle-Angle (AA) Similarity Theorem
c)
8.4 Side-Side-Side (SSS) Similarity Theorem
d)
7.11 Rhombus Diagonals Theorem
49.
If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.
a)
6.12 Hinge Theorem
b)
7.3 Parallelogram Opposite Sides Theorem
c)
6.10 Triangle Larger Angle Theorem
d)
8.4 Side-Side-Side (SSS) Similarity Theorem
50.
If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
a)
6.13 Converse of the Hinge Theorem
b)
7.2 Polygon Exterior Angles Theorem
c)
6.8 Triangle Midsegment Theorem
d)
9.4 45-45-90 Triangle Theorem
51.
The sum of the measures of the interior angles of a convex n-gon is (n − 2) ⋅ 180°.
a)
7.1 Polygon Interior Angles Theorem
b)
3.9 Transitive Property of Parallel Lines
c)
3.3 Alternate Exterior Angles Theorem
d)
5.8 Side-Side-Side (SSS) Congruence Theorem
52.
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°.
a)
7.2 Polygon Exterior Angles Theorem
b)
3.4 Consecutive Interior Angles Theorem
c)
7.15 Isosceles Trapezoid Base Angles Converse
d)
10.2 External Tangent Congruence Theorem
53.
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
a)
7.3 Parallelogram Opposite Sides Theorem
b)
6.3 Angle Bisector Theorem
c)
Corollary 7.4 Square Corollary
d)
5.6 Base Angles Theorem
54.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
a)
7.4 Parallelogram Opposite Angles Theorem
b)
2.1 Properties of Segment Congruence
c)
9.7 Geometric Mean (Altitude) Theorem
d)
10.1 Tangent Line to Circle Theorem
55.
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
a)
7.5 Parallelogram Consecutive Angles Theorem
b)
6.2 Converse of the Perpendicular Bisector Theorem
c)
7.18 Trapezoid Midsegment Theorem
d)
7.15 Isosceles Trapezoid Base Angles Converse
56.
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
a)
7.6 Parallelogram Diagonals Theorem
b)
6.6 Incenter Theorem
c)
Corollary 7.1 Corollary to the Polygon Interior Angles Theorem
d)
5.4 Third Angles Theorem
57.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
a)
7.7 Parallelogram Opposite Sides Converse
b)
7.10 Parallelogram Diagonals Converse
c)
9.3 Pythagorean Inequalities Theorem
d)
6.13 Converse of the Hinge Theorem
58.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
a)
7.8 Parallelogram Opposite Angles Converse
b)
9.9 Law of Sines
c)
10.3 Congruent Circles Theorem
d)
7.6 Parallelogram Diagonals Theorem
59.
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.
a)
7.9 Opposite Sides Parallel and Congruent Theorem
b)
6.8 Triangle Midsegment Theorem
c)
9.7 Geometric Mean (Altitude) Theorem
d)
7.5 Parallelogram Consecutive Angles Theorem
60.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
a)
7.10 Parallelogram Diagonals Converse
b)
7.18 Trapezoid Midsegment Theorem
c)
3.11 Perpendicular Transversal Theorem
d)
4.3 Reflections in Intersecting Lines Theorem
61.
The sum of the measures of the exterior angles of a convex
a)
Corollary 7.1 Corollary to the Polygon Interior Angles Theorem
b)
6.1 Perpendicular Bisector Theorem
c)
Corollary 7.4 Square Corollary
d)
8.3 Angle-Angle (AA) Similarity Theorem
62.
A quadrilateral is a rhombus if and only if it has four congruent sides
a)
Corollary 7.2 Rhombus Corollary
b)
10.7 Perpendicular Chord Bisector Theorem
c)
8.9 Triangle Angle Bisector Theorem
d)
2.2 Properties of Angle Congruence
63.
A quadrilateral is a rectangle if and only if it has four right angles
a)
Corollary 7.3 Rectangle Corollary
b)
9.3 Pythagorean Inequalities Theorem
c)
8.8 Three Parallel Lines Theorem
d)
10.20 Segments of Secants and Tangents Theorem
64.
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
a)
Corollary 7.4 Square Corollary
b)
3.11 Perpendicular Transversal Theorem
c)
8.2 Areas of Similar Polygons
d)
Corollary to the Triangle Sum Theorem
65.
A parallelogram is a rhombus if and only if its diagonals are perpendicular
a)
7.11 Rhombus Diagonals Theorem
b)
8.5 Side-Angle-Side (SAS) Similarity Theorem
c)
3.8 Consecutive Interior Angles Converse
d)
6.7 Centroid Theorem
66.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
a)
7.12 Rhombus Opposite Angles Theorem
b)
Corollary 7.3 Rectangle Corollary
c)
8.6 Triangle Proportionality Theorem
d)
Corollary to the Converse of the Base Angles Theorem
67.
A parallelogram is a rectangle if and only if its diagonals are congruent.
a)
7.13 Rectangle Diagonals Theorem
b)
6.8 Triangle Midsegment Theorem
c)
3.14 Slopes of Perpendicular Lines
d)
7.19 Kite Diagonals Theorem
68.
If a trapezoid is isosceles, then each pair of base angles is congruent
a)
7.14 Isosceles Trapezoid Base Angles Theorem
b)
7.3 Parallelogram Opposite Sides Theorem
c)
3.12 Lines Perpendicular to a Transversal Theorem
d)
6.8 Triangle Midsegment Theorem
69.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
a)
7.15 Isosceles Trapezoid Base Angles Converse
b)
Corollary 7.3 Rectangle Corollary
c)
7.11 Rhombus Diagonals Theorem
d)
7.20 Kite Opposite Angles Theorem
70.
A trapezoid is isosceles if and only if its diagonals are congruent.
a)
7.16 Isosceles Trapezoid Diagonals Theorem
b)
2.6 Vertical Angles Congruence Theorem
c)
8.4 Side-Side-Side (SSS) Similarity Theorem
d)
7.4 Parallelogram Opposite Angles Theorem
71.
A trapezoid is isosceles if and only if opposite angles are supplementary.
a)
7.17 Isosceles Trapezoid Opposite Angles Theorem
b)
9.9 Law of Sines
c)
7.16 Isosceles Trapezoid Diagonals Theorem
d)
7.9 Opposite Sides Parallel and Congruent Theorem
72.
The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
a)
7.18 Trapezoid Midsegment Theorem
b)
5.2 Exterior Angle Theorem
c)
8.8 Three Parallel Lines Theorem
d)
10.20 Segments of Secants and Tangents Theorem
73.
If a quadrilateral is a kite, then its diagonals are perpendicular.
a)
7.19 Kite Diagonals Theorem
b)
9.3 Pythagorean Inequalities Theorem
c)
7.13 Rectangle Diagonals Theorem
d)
8.9 Triangle Angle Bisector Theorem
74.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
a)
7.20 Kite Opposite Angles Theorem
b)
9.1 Pythagorean Theorem
c)
10.19 Segments of Secants Theorem
d)
6.1 Perpendicular Bisector Theorem
75.
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
a)
8.1 Perimeters of Similar Polygons
b)
Corollary 7.4 Square Corollary
c)
7.19 Kite Diagonals Theorem
d)
Corollary to the Converse of the Base Angles Theorem
76.
If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths.
a)
8.2 Areas of Similar Polygons
b)
Corollary to the Triangle Sum Theorem
c)
Corollary to the Base Angles Theorem
d)
7.10 Parallelogram Diagonals Converse
77.
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
a)
8.3 Angle-Angle (AA) Similarity Theorem
b)
3.11 Perpendicular Transversal Theorem
c)
8.7 Converse of the Triangle Proportionality Theorem
d)
3.6 Alternate Interior Angles Converse
78.
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
a)
8.4 Side-Side-Side (SSS) Similarity Theorem
b)
6.9 Triangle Longer Side Theorem
c)
5.8 Side-Side-Side (SSS) Congruence Theorem
d)
5.3 Properties of Triangle Congruence
79.
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
a)
8.5 Side-Angle-Side (SAS) Similarity Theorem
b)
5.2 Exterior Angle Theorem
c)
5.9 Hypotenuse-Leg (HL) Congruence Theorem
d)
7.16 Isosceles Trapezoid Diagonals Theorem
80.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
a)
8.6 Triangle Proportionality Theorem
b)
6.3 Angle Bisector Theorem
c)
2.2 Properties of Angle Congruence
d)
2.5 Congruent Complements Theorem
81.
If a line divides two sides of a triangle proportionality , then it is parallel to the third side.
a)
8.7 Converse of the Triangle Proportionality Theorem
b)
7.15 Isosceles Trapezoid Base Angles Converse
c)
Corollary 7.4 Square Corollary
d)
9.5 30°-60°-90° Triangle Theorem
82.
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
a)
8.8 Three Parallel Lines Theorem
b)
7.5 Parallelogram Consecutive Angles Theorem
c)
7.15 Isosceles Trapezoid Base Angles Converse
d)
5.2 Exterior Angle Theorem
83.
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
a)
8.9 Triangle Angle Bisector Theorem
b)
6.5 Circumcenter Theorem
c)
8.2 Areas of Similar Polygons
d)
8.4 Side-Side-Side (SSS) Similarity Theorem
84.
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
a)
9.1 Pythagorean Theorem
b)
6.8 Triangle Midsegment Theorem
c)
10.2 External Tangent Congruence Theorem
d)
9.7 Geometric Mean (Altitude) Theorem
85.
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
a)
9.2 Converse of the Pythagorean Theorem
b)
Corollary to the Triangle Sum Theorem
c)
4.2 Reflections in Parallel Lines Theorem
d)
7.12 Rhombus Opposite Angles Theorem
86.
For any △ABC, where c is the length of the longest side, the following statements are true.If c2 < a2 + b2 , then △ABC is acute.If c2 > a2 + b2, then △ABC is obtuse.
a)
9.3 Pythagorean Inequalities Theorem
b)
7.10 Parallelogram Diagonals Converse
c)
6.5 Circumcenter Theorem
d)
7.19 Kite Diagonals Theorem
87.
in a 45*-45*-90* triangle the hypotenuse is square root 2 times as long as each leg, the legs are congruent
a)
9.4 45-45-90 Triangle Theorem
b)
6.1 Perpendicular Bisector Theorem
c)
5.3 Properties of Triangle Congruence
d)
4.3 Reflections in Intersecting Lines Theorem
88.
In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √— 3 times as long as the shorter leg.
a)
9.5 30°-60°-90° Triangle Theorem
b)
9.6 Right Triangle Similarity Theorem
c)
6.13 Converse of the Hinge Theorem
d)
5.1 Triangle Sum Theorem
89.
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
a)
9.6 Right Triangle Similarity Theorem
b)
5.10 Angle-Side-Angle (ASA) Congruence Theorem
c)
8.5 Side-Angle-Side (SAS) Similarity Theorem
d)
2.4 Congruent Supplements Theorem
90.
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse.
a)
9.7 Geometric Mean (Altitude) Theorem
b)
8.3 Angle-Angle (AA) Similarity Theorem
c)
9.2 Converse of the Pythagorean Theorem
d)
10.7 Perpendicular Chord Bisector Theorem
91.
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
a)
9.8 Geometric Mean (Leg) Theorem
b)
Corollary 7.3 Rectangle Corollary
c)
3.10 Linear Pair Perpendicular Theorem
d)
8.9 Triangle Angle Bisector Theorem
92.
The Law of Sines can be written in either of the following forms for △ABC with sides of length a, b, and c. sin A — a = sin B — b = sin C — c a — sin A = b — sin B = c — sin C
a)
9.9 Law of Sines
b)
3.13 Slopes of Parallel Lines
c)
Corollary 7.3 Rectangle Corollary
d)
3.12 Lines Perpendicular to a Transversal Theorem
93.
If △ABC has sides of length a, b, and c, then the followingare true.a2 = b2 + c2 − 2bc cos Ab2 = a2 + c2 − 2ac cos Bc2 = a2 + b2 − 2ab cos C
a)
9.10 Law of Cosines
b)
10.5 Similar Circles Theorem
c)
10.4 Congruent Central Angles Theorem
d)
7.11 Rhombus Diagonals Theorem
94.
In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
a)
10.1 Tangent Line to Circle Theorem
b)
6.13 Converse of the Hinge Theorem
c)
4.3 Reflections in Intersecting Lines Theorem
d)
5.8 Side-Side-Side (SSS) Congruence Theorem
95.
Tangent segments from a common external point are congruent
a)
10.2 External Tangent Congruence Theorem
b)
5.11 Angle-Angle-Side (AAS) Congruence Theorem
c)
9.8 Geometric Mean (Leg) Theorem
d)
9.1 Pythagorean Theorem
96.
Two circles are congruent circles if and only if they have the same radius.
a)
10.3 Congruent Circles Theorem
b)
6.9 Triangle Longer Side Theorem
c)
3.8 Consecutive Interior Angles Converse
d)
5.6 Base Angles Theorem
97.
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.
a)
10.4 Congruent Central Angles Theorem
b)
3.5 Corresponding Angles Converse
c)
7.10 Parallelogram Diagonals Converse
d)
2.3 Right Angles Congruence Theorem
98.
All circles are similar
a)
10.5 Similar Circles Theorem
b)
7.20 Kite Opposite Angles Theorem
c)
Converse of the Angle Bisector Theorem
d)
2.3 Right Angles Congruence Theorem
99.
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
a)
10.6 Congruent Corresponding Chords Theorem
b)
7.12 Rhombus Opposite Angles Theorem
c)
7.7 Parallelogram Opposite Sides Converse
d)
3.9 Transitive Property of Parallel Lines
100.
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
a)
10.7 Perpendicular Chord Bisector Theorem
b)
2.4 Congruent Supplements Theorem
c)
6.1 Perpendicular Bisector Theorem
d)
8.9 Triangle Angle Bisector Theorem
101.
If one chord of a circle is a perpendicular bisector of another chord, then the first chord is a diameter.
a)
10.8 Perpendicular Chord Bisector Converse
b)
7.2 Polygon Exterior Angles Theorem
c)
9.7 Geometric Mean (Altitude) Theorem
d)
9.2 Converse of the Pythagorean Theorem
102.
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
a)
10.9 Equidistant Chords Theorem
b)
8.5 Side-Angle-Side (SAS) Similarity Theorem
c)
3.5 Corresponding Angles Converse
d)
2.5 Congruent Complements Theorem
103.
The measure of an inscribed angle is one half the measure of its intercepted arc
a)
10.10 Measure of an Inscribed Angle Theorem
b)
6.11 Triangle Inequality Theorem
c)
10.1 Tangent Line to Circle Theorem
d)
7.16 Isosceles Trapezoid Diagonals Theorem
104.
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
a)
10.11 Inscribed Angles of a Circle Theorem
b)
10.15 Angles Inside the Circle Theorem
c)
9.7 Geometric Mean (Altitude) Theorem
d)
10.5 Similar Circles Theorem
105.
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
a)
10.12 Inscribed Right Triangle Theorem
b)
7.15 Isosceles Trapezoid Base Angles Converse
c)
10.11 Inscribed Angles of a Circle Theorem
d)
8.1 Perimeters of Similar Polygons
106.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
a)
10.13 Inscribed Quadrilateral Theorem
b)
Corollary to the Triangle Sum Theorem
c)
10.5 Similar Circles Theorem
d)
10.14 Tangent and Intersected Chord Theorem
107.
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
a)
10.14 Tangent and Intersected Chord Theorem
b)
9.5 30°-60°-90° Triangle Theorem
c)
3.10 Linear Pair Perpendicular Theorem
d)
10.15 Angles Inside the Circle Theorem
108.
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
a)
10.15 Angles Inside the Circle Theorem
b)
Corollary 7.3 Rectangle Corollary
c)
8.5 Side-Angle-Side (SAS) Similarity Theorem
d)
Corollary to the Base Angles Theorem
109.
If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
a)
10.16 Angles Outside the Circle Theorem
b)
5.2 Exterior Angle Theorem
c)
5.8 Side-Side-Side (SSS) Congruence Theorem
d)
7.12 Rhombus Opposite Angles Theorem
110.
The measure of a circumscribed angle is equal to 180° minus the measure of the central angle that intercepts the same arc.
a)
10.17 Circumscribed Angle Theorem
b)
6.11 Triangle Inequality Theorem
c)
8.5 Side-Angle-Side (SAS) Similarity Theorem
d)
8.8 Three Parallel Lines Theorem
111.
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
a)
10.18 Segments of Chords Theorem
b)
10.15 Angles Inside the Circle Theorem
c)
6.5 Circumcenter Theorem
d)
7.17 Isosceles Trapezoid Opposite Angles Theorem
112.
If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.
a)
10.19 Segments of Secants Theorem
b)
9.6 Right Triangle Similarity Theorem
c)
3.13 Slopes of Parallel Lines
d)
10.6 Congruent Corresponding Chords Theorem
113.
If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
a)
10.20 Segments of Secants and Tangents Theorem
b)
6.8 Triangle Midsegment Theorem
c)
5.9 Hypotenuse-Leg (HL) Congruence Theorem
d)
3.4 Consecutive Interior Angles Theorem
100 %
