Congruence Practice Questions
Common Core (US) · Common Core Geometry · 150 free MCQs with instant results and detailed explanations.
150
Total
50
Easy
79
Medium
21
Hard
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Sample Questions from Congruence
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Q1
Easy
Two triangles are said to be congruent if they have the same shape and size. Which of the following statements accurately describes a method to prove that two triangles are congruent?
A.
Side-Angle-Side (SAS) criterion
B.
Angle-Side-Angle (ASA) criterion
C.
Angle-Angle (AA) criterion
D.
Side-Side-Side (SSS) criterion
Show Answer & Explanation
Correct Answer: D
The Side-Side-Side (SSS) criterion states that if all three sides of one triangle are equal in length to the corresponding sides of another triangle, then the triangles are congruent. This is a fundamental method to establish congruence.
Q2
Easy
Triangle ABC is congruent to triangle DEF. If the measure of angle A is 40 degrees and the measure of angle D is also 40 degrees, what can be concluded?
A.
Angle B is equal to angle E.
B.
Angle C is equal to angle F.
C.
The triangles are not congruent.
D.
The sides opposite angle A and angle D are equal.
Show Answer & Explanation
Correct Answer: D
Since triangle ABC is congruent to triangle DEF, corresponding angles are equal and corresponding sides are equal. Thus, the sides opposite angle A and angle D must be equal, confirming their congruence.
Q3
Easy
If two triangles have two sides that are equal and the angle between those sides is also equal, which congruence rule applies?
A.
Angle-Angle-Side (AAS)
B.
Side-Side-Angle (SSA)
C.
Side-Angle-Side (SAS)
D.
Side-Side-Side (SSS)
Show Answer & Explanation
Correct Answer: C
The Side-Angle-Side (SAS) congruence rule states that if two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle, then the triangles are congruent.
Q4
Medium
Two triangles are congruent if their corresponding sides and angles are equal. Which of the following criteria is NOT sufficient to prove that two triangles are congruent?
A.
Side-Side-Side (SSS)
B.
Angle-Angle (AA)
C.
Side-Angle-Side (SAS)
D.
Angle-Side-Angle (ASA)
Show Answer & Explanation
Correct Answer: B
The Angle-Angle (AA) criterion only establishes similarity, not congruence, because it does not provide information about the lengths of the sides.
Q5
Medium
If triangle XYZ is congruent to triangle ABC, which of the following statements is true?
A.
The angles of triangle ABC are half the angles of triangle XYZ.
B.
The sides of triangle ABC are twice the lengths of the sides of triangle XYZ.
C.
Angle X is congruent to angle A.
D.
Triangle ABC is similar to triangle XYZ but not congruent.
Show Answer & Explanation
Correct Answer: C
If two triangles are congruent, their corresponding angles are also congruent; thus, angle X is equal to angle A.
Q6
Medium
In triangle DEF, if DE = 10 cm, DF = 8 cm, and EF = 10 cm, what method can be used to determine if triangle DEF is isosceles?
A.
Check if two sides are equal.
B.
Check if all angles are equal.
C.
Use the Pythagorean theorem.
D.
Calculate the area of the triangle.
Show Answer & Explanation
Correct Answer: A
To determine if a triangle is isosceles, we need to check if at least two sides are equal. In this case, DE and EF are both 10 cm, confirming it is isosceles.
Q7
Medium
Which of the following pairs of triangles are congruent based on the criteria of Side-Angle-Side (SAS)?
A.
Triangle PQR with PQ = 5, QR = 7, and angle P = 60°, Triangle STU with ST = 5, TU = 7, and angle S = 60°
B.
Triangle ABC with AB = 6, AC = 8, and angle B = 45°, Triangle DEF with DE = 6, DF = 8, and angle E = 45°
C.
Triangle JKL with JK = 4, KL = 9, and angle J = 30°, Triangle MNO with MN = 4, NO = 9, and angle M = 30°
D.
Triangle XYZ with XY = 3, YZ = 4, and angle X = 90°, Triangle ABC with AB = 3, AC = 4, and angle A = 90°
Show Answer & Explanation
Correct Answer: A
In option A, the pairs satisfy the SAS criterion where two sides and the included angle are equal, confirming the triangles are congruent.
Q8
Hard
In triangle ABC, if angle A is congruent to angle D in triangle DEF, and angle B is congruent to angle E, which congruence criterion can be used to prove that triangle ABC is congruent to triangle DEF?
A.
ASA (Angle-Side-Angle)
B.
SAS (Side-Angle-Side)
C.
SSS (Side-Side-Side)
D.
AAA (Angle-Angle-Angle)
Show Answer & Explanation
Correct Answer: A
The ASA criterion states that 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 congruent. In this case, angle A and angle D are congruent, and angle B and angle E are congruent, allowing us to use ASA.
Q9
Hard
Two triangles, PQR and STU, have sides PQ = 5, QR = 7, RP = 8 and SU = 7, UT = 5, TS = 8. What can be concluded about the congruence of these triangles?
A.
Triangle PQR is congruent to triangle STU by SSS.
B.
Triangle PQR is congruent to triangle STU by SAS.
C.
Triangle PQR is not congruent to triangle STU.
D.
Triangle PQR is congruent to triangle STU by ASA.
Show Answer & Explanation
Correct Answer: A
The SSS (Side-Side-Side) criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Here, the sides match (5, 7, 8), confirming that triangle PQR is congruent to triangle STU by SSS.
Q10
Hard
In triangle ABC, angle A measures 30 degrees and angle B measures 70 degrees. If triangle DEF is congruent to triangle ABC, what is the measure of angle E in triangle DEF?
A.
30 degrees
B.
70 degrees
C.
80 degrees
D.
100 degrees
Show Answer & Explanation
Correct Answer: A
Since triangle DEF is congruent to triangle ABC, the corresponding angles are equal. Therefore, angle E in triangle DEF must also measure 30 degrees, matching angle A in triangle ABC.
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Congruence — Common Core (US) Common Core Geometry Practice Questions Online
This page contains 150 practice MCQs for the chapter Congruence in Common Core (US) Common Core Geometry. The questions are organized by difficulty — 50 easy, 79 medium, 21 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.