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WorksheetsGeometry Review Benchmark 2025
Total questions: 65
Worksheet time: 49mins
What is the sum of the interior angles of a triangle?
90°
180°
360°
270°
If a triangle has angles of 50° and 70°, what is the measure of the third angle?
30°
40°
60°
80°
What type of triangle has one angle that measures more than 90°?
Equilateral
Right
Acute
Obtuse
A triangle has angles of 20°, 30°, and x°. What is the value of x?
120°
130°
140°
150°
Which of the following is a property of parallelograms?
Opposite angles are supplementary
Opposite sides are congruent
Consecutive angles are equal
Diagonals are perpendicular
In a parallelogram, which statement is always true?
The diagonals bisect each other
The diagonals are congruent
The opposite sides are perpendicular
All angles are right angles
If one angle of a parallelogram is 70°, what is the measure of its consecutive angle?
70°
110°
180°
90°
A triangle has angles of 45°, 45°, and x°. What is the value of x?
90°
60°
45°
75°
Which of the following is true about the base angles of an isosceles triangle?
They are always equal to the vertex angle.
They are always different from each other.
They are always equal to each other.
They can be less than 30°.
In an isosceles triangle, which angles are congruent?
The base angles
The vertex angle
All angles
None of the angles
If an isosceles triangle has base angles of 55°, what is the measure of the vertex angle?
70°
80°
90°
110°
Which of the following triangles has angles that sum to 180°?
Triangle with angles 50°, 60°, 70°
Triangle with angles 90°, 90°, 0°
Triangle with angles 100°, 50°, 30°
Triangle with angles 80°, 80°, 30°
If an isosceles triangle has base angles of 75°, what is the measure of the vertex angle?
30°
70°
90°
110°
What is the relationship between the base angles and the vertex angle in an isosceles triangle?
The base angles are always larger.
The vertex angle is always larger.
The base angles are always equal to the vertex angle.
The base angles can never equal the vertex angle
Which property distinguishes an isosceles triangle from other types of triangles?
It has all angles equal.
It has at least two sides equal.
It has one right angle.
It has no congruent angles.
In an isosceles triangle, if the vertex angle is 100°, what is the measure of each base angle?
40°
50°
60°
70°
If the length of the third side of a triangle is 10 cm, what is the length of the segment connecting the midpoints of the other two sides?
5 cm
10 cm
15 cm
20 cm
In triangle ABC, if D and E are midpoints of sides AB and AC respectively, which statement is correct?
DE is longer than BC.
DE is equal to BC.
DE is half the length of BC.
DE is unrelated to BC.
What theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side?
Pythagorean Theorem
Midsegment Theorem
Triangle Inequality Theorem
Congruence Theorem
In triangle XYZ, if M and N are the midpoints of XY and XZ, respectively, and MN = 6 cm, what is the length of side YZ?
3 cm
6 cm
9 cm
12 cm
In triangle ABC, if the midpoints of sides AB and AC are joined to form segment DE, which of the following is NOT true?
DE is parallel to BC.
DE is half the length of BC.
DE can be longer than BC.
DE divides triangle ABC into two smaller triangles.
In a triangle, if you connect the midpoints of two sides, what is true about the segment formed?
It is parallel to the third side.
It is perpendicular to the third side.
It is equal in length to the third side.
It bisects the triangle.
What is the point where the medians of a triangle intersect called?
Circumcenter
Incenter
Centroid
Orthocenter
How many medians can be drawn in a triangle?
One
Two
Three
Four
If the midsegment of a triangle is 7 cm long, what is the length of the side it is parallel to?
3.5 cm
7 cm
14 cm
21 cm
If triangle ABC is similar to triangle DEF, which of the following statements is true regarding the lengths of their sides?
The sides are equal in length.
The sides are in a constant ratio.
The sides are different lengths with no relationship.
The sides are all proportional to 1:1.
When proving two triangles are similar using similarity transformations, what kind of transformations are involved?
Only rotations
Only translations
Rigid motions and dilations
Only reflections
Which similarity criterion can be used to establish triangle similarity with only one pair of equal angles and two pairs of proportional sides?
AA
SAS
SSS
AAS
If DE is parallel to BC in triangle ABC, and AD = 4 cm, DB = 6 cm, and AE = x cm, what is the length of EC?
4 cm
6 cm
9 cm
8 cm
Which statement is true about a line that divides two sides of a triangle proportionally?
It is parallel to the third side.
It is perpendicular to the third side.
It is equal to the length of the third side.
It is unrelated to the third side.
The Pythagorean Theorem states that in a right triangle: Mark only one oval.
a + b = c
a2+b2=c2
a2+b=c2
a+b2=c
In a right triangle, if the lengths of the legs are known, how can you find the length of the hypotenuse?
Add the lengths of the legs.
Subtract the lengths of the legs.
Use the Pythagorean Theorem.
Multiply the lengths of the legs.
If triangle ABC is inscribed in a semicircle, what type of triangle is formed when AB is the diameter?
Acute triangle
Obtuse triangle
Right triangle
Equilateral triangle
If a triangle has sides of lengths 9, 12, and 15, what is the relationship between this triangle and a triangle with sides 3, 4, and 5?
They are not similar.
They are similar by SSS.
They are congruent.
They are similar by SAS.
Which of the following statements is true about the sides of two similar triangles?
They are always equal.
They can be equal, but they must be proportional.
They are always proportional.
They are not related.
In triangle ABC, if angle A is equal to angle D and angle B is equal to angle E, what can be concluded?
Triangles ABC and DEF are congruent.
Triangles ABC and DEF are similar.
Triangles ABC and DEF are not related.
Triangles ABC and DEF have equal areas.
If the lengths of the legs of a right triangle are 7 cm and 24 cm, what is the length of the hypotenuse?
25 cm
26 cm
27 cm
28 cm
In triangle ABC, if AB = 8 cm, AC = 6 cm, and BC = 10 cm, is triangle ABC a right triangle?
Yes
No
Cannot determine
It depends on the angles.
If triangle ABC is similar to triangle DEF, and angle A measures 50°, what is the measure of angle D?
50°
60°
70°
80°
In triangle ABC, if angle A measures 30° and angle B measures 60°, what can be inferred about angle C?
It is 30°.
It is 60°.
It is 90°.
It is 90° or greater.
A parallelogram PQRS is shown. If m∠P = 110°, what is the value of m∠Q?
30°
50°
70°
110°
A parallelogram PQRS is shown. If PQ = 5 units, what is the length of RS?
2 units
4 units
5 units
10 units
In a triangle, if two angles are equal, what can be inferred about the sides opposite those angles?
They are unequal.
They are equal.
They are proportional.
They can be any length.
How can the Pythagorean Theorem be proved using similarity?
By showing that the triangles are congruent.
By using proportionality of sides in similar triangles.
By constructing an angle bisector.
By using the Law of Cosines.
If triangle ABC is a right triangle and the altitude from C meets side AB at point D, how are triangles ACD and BCD related?
They are similar.
They are congruent.
They are not related.
They are the same triangle.
In triangle ABC, with a right angle at C, if AC = 6 and BC = 8, what is the length of hypotenuse AB?
10
12
14
16
Which theorem can be used to prove that a quadrilateral is a parallelogram?
Both pairs of opposite sides are congruent
The diagonals are perpendicular
One pair of opposite sides is congruent and perpendicular
All sides are congruent
In a parallelogram, if one diagonal measures 10 cm and the other measures 14 cm, which statement is true about their intersection?
The diagonals divide the parallelogram into four congruent triangles
The diagonals are congruent
Each diagonal is divided into two equal parts
The diagonals are perpendicular
If the diagonals of a parallelogram are congruent, what special type of parallelogram is it?
Rhombus
Rectangle
Trapezoid
Kite
Which condition is sufficient to prove that a quadrilateral is a parallelogram?
The diagonals bisect each other
Only one pair of opposite sides is parallel
The diagonals are congruent
Only one pair of angles is congruent
In parallelogram ABCD, diagonal AC bisects ∠BAD. What type of parallelogram is ABCD?
Rectangle
Square
Rhombus
Trapezoid
G.G-CO.C.11
If two consecutive angles of a parallelogram are in the ratio 3:2, what is the measure of the larger angle?
72°
108°
120°
144°
G.G-CO.C.11
Which of the following statements is false about parallelograms?
Opposite sides are parallel
Consecutive angles are supplementary
Diagonals always form right angles
Opposite angles are congruent
G.G-CO.C.11
Which of the following is true about the opposite sides of a parallelogram?
They are perpendicular
They are congruent
They are unequal
They form right angles
G.G-CO.C.11
If the opposite angles of a quadrilateral are congruent, which of the following can we conclude?
The quadrilateral is a trapezoid
The quadrilateral is a parallelogram
The quadrilateral is a rectangle
The quadrilateral is a rhombus
G.G-CO.C.11
Which of the following properties is unique to the diagonals of a parallelogram?
They are equal in length
They bisect each other
They are perpendicular
They form congruent angles
G.G-CO.C.11
In a rectangle, which statement is true about the diagonals?
They bisect each other and are congruent
They bisect each other and are perpendicular
They are congruent but do not bisect each other
They are perpendicular but not congruent
G.G-CO.C.11
Which of the following proves that a quadrilateral is a rectangle?
The diagonals are perpendicular
Opposite angles are congruent
The diagonals are congruent
Opposite sides are parallel
G.G-CO.C.11
If one angle of a parallelogram is a right angle, what type of parallelogram is it?
Rhombus
Rectangle
Square
Trapezoid
G.G-CO.C.11
Which of the following is NOT a property of parallelograms?
Opposite sides are parallel and congruent
Opposite angles are congruent
The diagonals are always congruent
The diagonals bisect each other
G.G-CO.C.11
In parallelogram ABCD, if AC=12 and BD=16, what is the length of the segments formed by the intersection of the diagonals?
12 and 16
6 and 8
8 and 8
6 and 6
G.G-CO.C.11
In parallelogram ABCD, ∠A measures 70∘. What is the measure of ∠C?
70∘
110∘
90∘
180∘
G.G-CO.C.10
In a triangle, if the angles are represented as x, y, and z, which equation represents their relationship?
x + y = z
x + y + z = 180°
x + y + z = 360°
x + y = 90°
G.G-CO.C.10
If a triangle has angles of 50° and 70°, what is the measure of the third angle?
30°
40°
60°
80°
G.G-CO.C.10
If one angle of a triangle is 60° and another angle is 80°, what is the measure of the third angle?
40°
50°
60°
70°
