Geometry Practice Test: Triangle Congruence (SSS, SAS, ASA, AAS, HL)
- Triangle Congruence
- 10 questions
- 13 minutes
This test focuses on proving triangles congruent and using the result. Tip: mark the given parts on a quick sketch and check whether a given angle lies between the two given sides.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
In △ABC and △DEF, AB ≅ DE, BC ≅ EF and ∠B ≅ ∠E.
Which criterion proves that △ABC ≅ △DEF?
Correct answer: C
Angle B lies between sides AB and BC, so the given parts are two sides and the included angle: SAS. Only two pairs of sides are given, so SSS does not apply.
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Question 2
In △ABC and △DEF, ∠A ≅ ∠D, ∠B ≅ ∠E and BC ≅ EF.
Which criterion proves that the triangles are congruent?
Correct answer: A
Side BC is not between angles A and B (the included side would be AB), so the criterion is AAS, not ASA.
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Question 3
In △ABC and △DEF, ∠A ≅ ∠D and AB ≅ DE.
Which additional fact would let you prove the triangles congruent by ASA?
Correct answer: D
ASA needs two angles and the side between them. Side AB lies between angles A and B, so ∠B ≅ ∠E is needed. ∠C ≅ ∠F would give AAS, and AC ≅ DF would give SAS.
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Question 4
Segments AB and CD bisect each other at point M.
Which criterion proves that △AMC ≅ △BMD?
Correct answer: B
Because M is the midpoint of both segments, AM ≅ BM and CM ≅ DM. The angles ∠AMC and ∠BMD are vertical angles, so they are congruent, and they lie between those sides: SAS.
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Question 5
In quadrilateral ABCD, AB ≅ AD and CB ≅ CD. Diagonal AC is drawn, and △ABC ≅ △ADC by SSS.
Which statement must be true?
Correct answer: C
In the congruence △ABC ≅ △ADC, angle BAC corresponds to angle DAC, so they are congruent by CPCTC. The other statements compare parts that do not correspond.
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Question 6
△JKL ≅ △RST, JK = 3x − 4 and RS = 2x + 5.
What is the length of JK?
Correct answer: C
Corresponding sides are congruent: 3x − 4 = 2x + 5, so x = 9 and JK = 3(9) − 4 = 23. The choice 9 stops at the value of x.
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Question 7
△ABC ≅ △PQR, m∠A = (5y − 10)°, m∠P = (3y + 14)° and m∠B = 70°.
What is m∠R?
Correct answer: D
From 5y − 10 = 3y + 14, y = 12 and m∠A = 50°. Then m∠C = 180° − 50° − 70° = 60°, and ∠R corresponds to ∠C, so m∠R = 60°.
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Question 8
In △ABC, AB ≅ AC. Segment AD is drawn perpendicular to BC, with D on BC.
Using only AB ≅ AC, AD ⊥ BC and AD ≅ AD, which criterion proves △ABD ≅ △ACD?
Correct answer: A
Both triangles are right triangles with right angles at D. Their hypotenuses AB and AC are congruent and they share leg AD, which is exactly HL. The given angle is not between the two given sides, so SAS does not apply.
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Question 9
A proof that △ABD ≅ △CBD includes the statement BD ≅ BD.
Which reason justifies this statement?
Correct answer: D
A segment shared by two triangles is congruent to itself, which is the Reflexive Property. The Symmetric Property turns AB ≅ CD into CD ≅ AB, which is a different statement.
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Question 10
△ABC is mapped onto △DEF by a rotation followed by a translation.
Which statement must be true?
Correct answer: A
Rotations and translations are rigid motions: they keep all lengths and angle measures, so the image is congruent to the original. Neither one reverses orientation; only reflections do.
Questions you leave blank are not counted as wrong.
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