Quiz about Geometry Quiz

Question 1

What are Corresponding Angles?

Accepted Answer

Pairs of angles formed by two lines and a transversal that make an F pattern

Answer

Pairs of angles formed by two lines and a transversal that make a C pattern

Answer

Pairs of angles formed by two lines and a transversal that make a Z pattern

Answer

Triangles in which corresponding parts (sides and angles) are equal in measure

Question 2

What are Same-side Interior Angles?

Accepted Answer

Pairs of angles formed by two lines and a transversal that make an F pattern

Answer

Pairs of angles formed by two lines and a transversal that make a C pattern

Answer

Pairs of angles formed by two lines and a transversal that make a Z pattern

Answer

Triangles in which corresponding parts (sides and angles) are equal in measure

Question 3

What are Alternate Interior Angles?

Accepted Answer

Pairs of angles formed by two lines and a transversal that make a Z pattern

Answer

Pairs of angles formed by two lines and a transversal that make an F pattern

Answer

Pairs of angles formed by two lines and a transversal that make a C pattern

Answer

Triangles in which corresponding parts (sides and angles) are equal in measure

Question 4

What are Congruent Triangles?

Accepted Answer

Triangles in which corresponding parts (sides and angles) are equal in measure

Answer

Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion

Answer

A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure

Answer

A ray, line or segment that divides a segment into two parts of equal measure

Question 5

What are Similar Triangles?

Accepted Answer

Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion

Answer

Triangles in which corresponding parts (sides and angles) are equal in measure

Answer

A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure

Answer

A ray, line or segment that divides a segment into two parts of equal measure

Question 6

What is an Angle Bisector?

Accepted Answer

A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure

Answer

A ray, line or segment that divides a segment into two parts of equal measure

Answer

The sides of equal measure in an isosceles triangle

Answer

The third side of an isosceles triangle

Question 7

What is a Segment Bisector?

Accepted Answer

A ray, line or segment that divides a segment into two parts of equal measure

Answer

A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure

Answer

The sides of equal measure in an isosceles triangle

Answer

The third side of an isosceles triangle

Question 8

What are the Legs of an Isosceles Triangle?

Accepted Answer

The sides of equal measure in an isosceles triangle

Answer

The third side of an isosceles triangle

Answer

A line that bisects a segment and is perpendicular to it

Answer

A segment from a vertex of a triangle perpendicular to the line containing the opposite side

Question 9

What is the Base of an Isosceles Triangle?

Accepted Answer

The third side of an isosceles triangle

Answer

The sides of equal measure in an isosceles triangle

Answer

A line that bisects a segment and is perpendicular to it

Answer

A segment from a vertex of a triangle perpendicular to the line containing the opposite side

Question 10

What does Equiangular mean?

Accepted Answer

Having angles that are all equal in measure

Answer

A line that bisects a segment and is perpendicular to it

Answer

A segment from a vertex of a triangle perpendicular to the line containing the opposite side

Answer

The third side of an isosceles triangle

Question 11

What is a Perpendicular Bisector?

Accepted Answer

A line that bisects a segment and is perpendicular to it

Answer

A segment from a vertex of a triangle perpendicular to the line containing the opposite side

Answer

The third side of an isosceles triangle

Answer

The sides of equal measure in an isosceles triangle

Question 12

What is an Altitude in a triangle?

Accepted Answer

A segment from a vertex of a triangle perpendicular to the line containing the opposite side

Answer

A line that bisects a segment and is perpendicular to it

Answer

The third side of an isosceles triangle

Answer

The sides of equal measure in an isosceles triangle

Question 13

What is the definition of the geometric mean?

Accepted Answer

The value of x in proportion a/x = x/b where a, b, and x are positive numbers

Answer

The ratio of the side opposite the angle to the measure of the hypotenuse

Answer

The ratio of the side adjacent to the angle to the measure of the hypotenuse

Answer

The ratio of the side opposite the angle to the measure of the side adjacent

Question 14

What is the sine of an acute angle in a right triangle?

Accepted Answer

The ratio of the side opposite the angle to the measure of the hypotenuse

Answer

The ratio of the side adjacent to the angle to the measure of the hypotenuse

Answer

The ratio of the side opposite the angle to the measure of the side adjacent

Answer

The value of x in proportion a/x = x/b where a, b, and x are positive numbers

Question 15

What is the cosine of an acute angle in a right triangle?

Accepted Answer

The ratio of the side adjacent to the angle to the measure of the hypotenuse

Answer

The ratio of the side opposite the angle to the measure of the hypotenuse

Answer

The ratio of the side opposite the angle to the measure of the side adjacent

Answer

The value of x in proportion a/x = x/b where a, b, and x are positive numbers

Question 16

What is the tangent of an acute angle in a right triangle?

Accepted Answer

The ratio of the side opposite the angle to the measure of the side adjacent

Answer

The ratio of the side opposite the angle to the measure of the hypotenuse

Answer

The ratio of the side adjacent to the angle to the measure of the hypotenuse

Answer

The value of x in proportion a/x = x/b where a, b, and x are positive numbers

Question 17

What does the Addition Property of Equality state?

Accepted Answer

If the same number is added to equal numbers, then the sums are equal

Answer

If the same number is subtracted from equal numbers, then the differences are equal

Answer

If equal numbers are multiplied by the same number, then the products are equal

Answer

If equal numbers are divided by the same number, then the quotients are equal

Question 18

What does the Subtraction Property of Equality state?

Accepted Answer

If the same number is subtracted from equal numbers, then the differences are equal

Answer

If the same number is added to equal numbers, then the sums are equal

Answer

If equal numbers are multiplied by the same number, then the products are equal

Answer

If equal numbers are divided by the same number, then the quotients are equal

Question 19

What does the Multiplication Property of Equality state?

Accepted Answer

If equal numbers are multiplied by the same number, then the products are equal

Answer

If the same number is added to equal numbers, then the sums are equal

Answer

If the same number is subtracted from equal numbers, then the differences are equal

Answer

If equal numbers are divided by the same number, then the quotients are equal

Question 20

What does the Division Property of Equality state?

Accepted Answer

If equal numbers are divided by the same number, then the quotients are equal

Answer

If the same number is added to equal numbers, then the sums are equal

Answer

If the same number is subtracted from equal numbers, then the differences are equal

Answer

If equal numbers are multiplied by the same number, then the products are equal

Question 21

What does the Reflexive Property of Equality state?

Accepted Answer

A number is equal to itself

Answer

If a = b then b = a

Answer

If values are equal, then one value may be substituted for the other

Answer

If a = b and b = c then a = c

Question 22

What does the Symmetric Property of Equality state?

Accepted Answer

If a = b then b = a

Answer

A number is equal to itself

Answer

If values are equal, then one value may be substituted for the other

Answer

If a = b and b = c then a = c

Question 23

What does the Substitution Property of Equality state?

Accepted Answer

If values are equal, then one value may be substituted for the other

Answer

A number is equal to itself

Answer

If a = b then b = a

Answer

If a = b and b = c then a = c

Question 24

What does the Transitive Property of Equality state?

Accepted Answer

If a = b and b = c then a = c

Answer

A number is equal to itself

Answer

If a = b then b = a

Answer

If values are equal, then one value may be substituted for the other

Question 25

What does the Distributive Property state?

Accepted Answer

a(b + c) = ab + ac

Answer

If a = b and b = c then a = c

Answer

If values are equal, then one value may be substituted for the other

Answer

If a = b then b = a

Question 26

What does the Angle Addition Postulate state?

Accepted Answer

For any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts.

Answer

If two angles form a linear pair, then they are supplementary.

Answer

If two angles are supplements of the same angle, then they are congruent.

Answer

Vertical angles are equal in measure.

Question 27

According to the Linear Pair Theorem, what is true if two angles form a linear pair?

Accepted Answer

They are supplementary.

Answer

They are congruent.

Answer

They are equal in measure.

Answer

They are complementary.

Question 28

What does the Right Angle Congruence Theorem state?

Accepted Answer

All right angles are congruent.

Answer

Vertical angles are equal in measure.

Answer

If two angles are complements of the same angle, then they are congruent.

Answer

If two angles form a linear pair, then they are supplementary.

Question 29

What does the Angle Bisector Theorem state?

Accepted Answer

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Answer

If two angles are supplements of the same angle, then they are congruent.

Answer

If two angles form a linear pair, then they are supplementary.

Answer

Vertical angles are equal in measure.

Question 30

What does the Segment Addition Postulate state?

Accepted Answer

For any segment, the measure of the whole is equal to the sum of the measures of its non-overlapping parts.

Answer

Through any two points there is exactly one line.

Answer

If two lines intersect, then they intersect at exactly one point.

Answer

If two parallel lines are intersected by a transversal, then the corresponding angles are equal in measure.

Question 31

What does the Corresponding Angles Postulate state?

Accepted Answer

If two parallel lines are intersected by a transversal, then the corresponding angles are equal in measure.

Answer

If two lines intersect, then they intersect at exactly one point.

Answer

If two angles form a linear pair, then they are supplementary.

Answer

Vertical angles are equal in measure.

Question 32

What does the Postulate state about a point not on a given line?

Accepted Answer

There is one and only one line parallel to the given line.

Answer

There are no lines parallel to the given line.

Answer

There are infinitely many lines parallel to the given line.

Answer

There is one and only one line perpendicular to the given line.

Question 33

According to the Alternate Interior Angles Theorem, what happens when two parallel lines are intersected by a transversal?

Accepted Answer

Alternate interior angles are equal in measure.

Answer

Alternate interior angles are supplementary.

Answer

Alternate exterior angles are equal in measure.

Answer

Same-side interior angles are equal in measure.

Question 34

What does the Same-side Interior Angles Theorem state about two parallel lines intersected by a transversal?

Accepted Answer

Same-side interior angles are supplementary.

Answer

Same-side interior angles are equal in measure.

Answer

Same-side interior angles are congruent.

Answer

Same-side interior angles are complementary.

Question 35

What is the conclusion of the Converse of Alternate Interior Angles Theorem if two lines are intersected by a transversal and alternate interior angles are equal in measure?

Accepted Answer

The lines are parallel.

Answer

The lines are perpendicular.

Answer

The lines are skew.

Answer

The lines are congruent.

Question 36

According to the Perpendicular Transversal Theorem, what happens if a transversal is perpendicular to one of two parallel lines?

Accepted Answer

It is perpendicular to the other one.

Answer

It is parallel to the other one.

Answer

It is congruent to the other one.

Answer

It is supplementary to the other one.

Question 37

What does the Parallel Lines Theorem state about two nonvertical lines in a coordinate plane?

Accepted Answer

They are parallel if they have the same slope.

Answer

They are parallel if they have the same y-intercept.

Answer

They are parallel if they have the same x-intercept.

Answer

They are parallel if they have the same length.

Question 38

According to the Perpendicular Lines Theorem, when are two nonvertical lines perpendicular in a coordinate plane?

Accepted Answer

If the product of their slopes is -1.

Answer

If the product of their slopes is 1.

Answer

If the product of their slopes is 0.

Answer

If the product of their slopes is undefined.

Question 39

What does the Two-Transversals Proportionality Corollary state about three or more parallel lines intersecting two transversals?

Accepted Answer

They divide the transversals proportionally.

Answer

They divide the transversals equally.

Answer

They divide the transversals perpendicularly.

Answer

They divide the transversals congruently.

Question 40

If two angles of one triangle are equal in measure to two angles of another triangle, then the two triangles are:

Accepted Answer

Similar

Answer

Congruent

Answer

Right-angled

Answer

Isosceles

Question 41

If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are:

Accepted Answer

Similar

Answer

Congruent

Answer

Right-angled

Answer

Isosceles

Question 42

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are:

Accepted Answer

Similar

Answer

Congruent

Answer

Right-angled

Answer

Isosceles

Question 43

If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are:

Accepted Answer

Congruent

Answer

Right-angled

Answer

Similar

Answer

Isosceles

Question 44

If two sides and the included angle of one triangle are equal in measure to the corresponding sides and angle of another triangle, then the triangles are:

Accepted Answer

Congruent

Answer

Right-angled

Answer

Similar

Answer

Isosceles

Question 45

If three sides of one triangle are equal in measure to the corresponding sides of another triangle, then the triangles are:

Accepted Answer

Congruent

Answer

Right-angled

Answer

Similar

Answer

Isosceles

Question 46

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are:

Accepted Answer

Congruent

Answer

Right-angled

Answer

Similar

Answer

Isosceles

Question 47

The acute angles of a right triangle are:

Accepted Answer

Complementary

Answer

Supplementary

Answer

Congruent

Answer

Similar

Question 48

An exterior angle of a triangle is equal in measure to the sum of the measures of its two remote:

Accepted Answer

Interior angles

Answer

Exterior angles

Answer

Right angles

Answer

Acute angles

Question 49

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides:

Accepted Answer

Proportionally

Answer

Equally

Answer

Congruently

Answer

Complementarily

Question 50

If a line divides two sides of a triangle proportionally, then it is parallel to the:

Accepted Answer

Third side

Answer

First side

Answer

Second side

Answer

Fourth side

Question 51

What does the Triangle Angle Bisector Theorem state?

Accepted Answer

An angle bisector of a triangle divides the opposite sides into two segments whose lengths are proportional to the lengths of the other two sides.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle, then the triangles are congruent.

Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Question 52

According to the Angle-Angle-Side Congruence Theorem (AAS), when are two triangles congruent?

Accepted Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle.

Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

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.

Question 53

What does the Hypotenuse-Leg Congruence Theorem (HL) state?

Accepted Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle, then the triangles are congruent.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

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.

Question 54

What does the Isosceles Triangle Theorem state?

Accepted Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle, then the triangles are congruent.

Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Answer

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.

Question 55

What is the Converse of the Isosceles Triangle Theorem?

Accepted Answer

If two angles of a triangle are equal in measure, then the sides opposite those angles are equal in measure.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle, then the triangles are congruent.

Question 56

What does the Pythagorean Theorem state?

Accepted Answer

In any right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle, then the triangles are congruent.

Answer

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Question 57

What does the Circumcenter Theorem state?

Accepted Answer

The circumcenter of a triangle is equidistant from the vertices of the triangle.

Answer

The incenter of a triangle is equidistant from the sides of the triangle.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle.

Question 58

What does the Incenter Theorem state?

Accepted Answer

The incenter of a triangle is equidistant from the sides of the triangle.

Answer

The circumcenter of a triangle is equidistant from the vertices of the triangle.

Answer

If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Answer

If two angles and a non-included side of one triangle are equal in measure to the corresponding angles and side of another triangle.

Question 59

What is the centroid theorem of a triangle?

Accepted Answer

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.

Answer

The centroid of a triangle is located 1/3 of the distance from each vertex to the midpoint of the opposite side.

Answer

The centroid of a triangle is located at the midpoint of each side.

Answer

The centroid of a triangle is located at the intersection of the medians.

Question 60

What does the Triangle Midsegment Theorem state?

Accepted Answer

A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side.

Answer

A midsegment of a triangle is parallel to a side of the triangle, and its length is equal to the length of that side.

Answer

A midsegment of a triangle is perpendicular to a side of the triangle, and its length is half the length of that side.

Answer

A midsegment of a triangle is perpendicular to a side of the triangle, and its length is equal to the length of that side.

Question 61

According to the Triangle Inequality Theorem, what is true about the side lengths of a triangle?

Accepted Answer

The sum of any two side lengths of a triangle is greater than the third side length.

Answer

The sum of any two side lengths of a triangle is less than the third side length.

Answer

The sum of any two side lengths of a triangle is equal to the third side length.

Answer

The sum of any two side lengths of a triangle is not related to the third side length.

Question 62

What does the Law of Sines state for any triangle ABC with side lengths a, b, and c?

Accepted Answer

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Answer

$\frac{a}{\cos A} = \frac{b}{\cos B} = \frac{c}{\cos C}$

Answer

$\frac{a}{\tan A} = \frac{b}{\tan B} = \frac{c}{\tan C}$

Answer

$\frac{a}{\cot A} = \frac{b}{\cot B} = \frac{c}{\cot C}$

Question 63

What does the Converse of the Pythagorean Theorem state?

Accepted Answer

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

Answer

If the sum of the squares of the lengths of two sides of a triangle is greater than the square of the length of the third side, then the triangle is a right triangle.

Answer

If the sum of the squares of the lengths of two sides of a triangle is less than the square of the length of the third side, then the triangle is a right triangle.

Answer

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is an obtuse triangle.

Question 64

Through any three noncollinear points there is exactly one plane containing them. This is an example of which geometric concept?

Accepted Answer

Postulate

Answer

Theorem

Answer

Definition

Answer

Corollary

Geometry Quiz

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