Mathematics

Triangle Congruence Quiz: Practice ASA, SAS, SSS, and AAS

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Use this triangle congruence quiz to decide when two triangles are congruent by ASA, SAS, SSS, or AAS, with instant feedback and clear steps. After you practice here, strengthen proofs in triangle congruence proofs practice, and review related ideas in similarity and congruence tests and right triangle similarity quiz.

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Paper art illustration with four labelled triangles ASA SAS SSS AAS on teal background, quiz on triangle congruence
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1Which triangle congruence postulate uses two angles and the included side?
2Which of the following is sufficient to prove two triangles are congruent based solely on side lengths?
3Which of the following is NOT a valid triangle congruence criterion?
4What does the AAS congruence criterion stand for?
5If in two triangles ?A = ?D, AB = DE, and ?B = ?E, which congruence postulate applies?
6Two triangles have AB = DE, BC = EF, and ?B = ?E. Which congruence criterion proves them congruent?
7In triangles ABC and DEF, ?A = ?D, AC = DF, and ?C = ?F. Which postulate justifies their congruence?
8Given triangles with sides AB = DE, BC = EF, and CA = FD, which congruence rule applies?
9What does CPCTC stand for in triangle congruence proofs?
10If ?A = ?D, ?B = ?E, and BC = EF in two triangles, which congruence criterion is used?
11Given triangles ABC and DEF with AB = DE, ?B = ?E, and ?C = ?F, which congruence postulate applies?
12Which of these criteria cannot prove two triangles are congruent?
13Triangle ABC has vertices A(0,0), B(3,0), C(3,4). Triangle DEF has D(1,1), E(4,1), F(4,5). Which congruence criterion applies?
14In proving the base angles of an isosceles triangle are congruent, after applying SAS to two smaller triangles, which principle confirms the base angles are equal?
15When given two sides and a non-included angle (SSA) with side a shorter than side b but longer than b·sin(C), two distinct triangles satisfy the conditions.
Learning Goals

Study Outcomes

  1. Understand Triangle Congruence Postulates -

    Gain clarity on the ASA, SAS, SSS, and AAS criteria and their role in establishing triangle congruency.

  2. Identify Applicable Theorems -

    Analyze pairs of triangles to determine whether ASA, SAS, SSS, or AAS applies based on given sides and angles.

  3. Apply Congruence Criteria -

    Use the relevant postulates to prove two triangles are congruent in structured, step-by-step solutions.

  4. Construct Logical Proofs -

    Develop clear, coherent geometric proofs that demonstrate triangle congruency using these fundamental theorems.

  5. Evaluate Triangle Pairs -

    Assess various triangle configurations to confirm congruency and understand when theorems cannot be applied.

  6. Solve for Unknown Elements -

    Determine missing angles or side lengths by leveraging established congruence proofs.

Study Guide

Cheat Sheet

  1. SSS Congruence -

    The SSS theorem states that if all three pairs of corresponding sides are equal, then the triangles are congruent (Euclid's Elements, Prop. I.4). For example, if AB=DE, BC=EF, and CA=FD then ΔABC≅ΔDEF; remember "Side-Side-Side seals the deal!" (MIT OpenCourseWare).

  2. SAS Congruence -

    According to Khan Academy, SAS holds when two sides and the included angle of one triangle match two sides and the included angle of another (ASA SAS SSS AAS synergy). For instance, AB=DE, ∠B=∠E, and BC=EF guarantee ΔABC≅ΔDEF - just think "Side-Angle-Side, it fits just right."

  3. ASA Congruence -

    The ASA theorem requires two angles and the included side to be equal, proving congruence (University of Texas Geometry Lab). If ∠A=∠D, AB=DE, and ∠B=∠E, then ΔABC≅ΔDEF - use "Angle-Side-Angle, congruence made easy."

  4. AAS Congruence -

    AAS applies when two angles and a non-included side match, ensuring triangles are congruent (NCERT Curriculum). For example, if ∠A=∠D, ∠B=∠E, and BC=EF, then ΔABC≅ΔDEF; recall "Any two Angles plus a Side = congruence ride."

  5. Avoiding SSA Ambiguity -

    Unlike valid ASA, SAS, SSS, and AAS, the SSA (or ASS) case can create two possible triangles, so it fails to guarantee congruence (Stanford University Geometry Notes). Keep the mnemonic "Side-Side-Angle slips away" in mind when sorting aas sss sas asa theorems.

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Updated Feb 22, 2026