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Quizzes > Mathematics > Geometry

Ready to Ace the ASA, SAS, SSS & AAS Triangle Quiz?

Think you can master AAS SSS SAS ASA? Dive into the quiz!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration with four labelled triangles ASA SAS SSS AAS on teal background, quiz on triangle congruence

This triangle congruence quiz helps you practice ASA, SAS, SSS, and AAS and decide when two triangles are congruent. Use practice questions with quick feedback, then check step‑by‑step solutions to spot gaps before an exam and build speed faster today.

Which triangle congruence postulate uses two angles and the included side?
SAS
SSS
ASA
AAS
The ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. The included side is the side between the two given angles. This criterion guarantees a unique triangle is formed.
Which of the following is sufficient to prove two triangles are congruent based solely on side lengths?
ASA
AAS
SSS
SAS
The SSS postulate (Side - Side - Side) states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. No angles need to be measured because side lengths alone fully determine the shape. This is one of the primary congruence tests.
Which of the following is NOT a valid triangle congruence criterion?
ASA
SSA
SAS
SSS
SSA (Side-Side-Angle) is not a valid congruence criterion because the angle is not included between the two given sides, which can create an ambiguous case with two possible triangles. The other three postulates (SAS, ASA, SSS) guarantee a unique triangle.
What does the AAS congruence criterion stand for?
Angle-Angle-Side
Angle-Side-Angle
Side-Angle-Side
Side-Side-Angle
AAS stands for Angle - Angle - Side, which means two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle. Even though the side is non-included, the triangles are still uniquely determined.
If in two triangles ?A = ?D, AB = DE, and ?B = ?E, which congruence postulate applies?
AAS
SSS
ASA
SAS
Since AB is the side included between the two equal angles ?A and ?B, the ASA postulate applies. The included side ensures the triangles are congruent. ASA is one of the basic congruence criteria.
Two triangles have AB = DE, BC = EF, and ?B = ?E. Which congruence criterion proves them congruent?
SAS
AAS
ASA
SSS
The SAS postulate applies because two sides (AB and BC) and the included angle ?B are congruent to the corresponding parts in the other triangle. The included angle guarantees a unique triangle.
In triangles ABC and DEF, ?A = ?D, AC = DF, and ?C = ?F. Which postulate justifies their congruence?
AAS
SSS
ASA
SAS
The side AC is included between the angles at A and C, so this fits the ASA postulate. Two angles and the included side guarantee triangle congruence.
Given triangles with sides AB = DE, BC = EF, and CA = FD, which congruence rule applies?
AAS
SSS
SAS
ASA
With all three corresponding sides equal, the SSS postulate applies. This ensures the triangles are congruent without measuring any angles.
What does CPCTC stand for in triangle congruence proofs?
Corresponding Parts of Congruent Triangles are Congruent
Corresponding Points of Congruent Triangles are Combined
Congruent Parts of Corresponding Triangles are Constant
Chosen Parts of Congruent Triangles are Congruent
CPCTC is the abbreviation for "Corresponding Parts of Congruent Triangles are Congruent." Once two triangles are proven congruent, all their corresponding sides and angles are congruent. It's a common justification step in proofs.
If ?A = ?D, ?B = ?E, and BC = EF in two triangles, which congruence criterion is used?
SAS
SSS
AAS
ASA
Since two angles and a non-included side (BC) are congruent, the AAS postulate applies. AAS guarantees triangle congruence when the side is not between the given angles.
Given triangles ABC and DEF with AB = DE, ?B = ?E, and ?C = ?F, which congruence postulate applies?
AAS
SSS
ASA
SAS
Here AB is not included between ?B and ?C, so we have two angles and the non-included side AB. This matches the AAS postulate, which still guarantees congruence.
Which of these criteria cannot prove two triangles are congruent?
AAA
ASA
SAS
SSS
AAA (Angle - Angle - Angle) only guarantees triangle similarity, not congruence, because the size may differ. The other criteria (SAS, ASA, SSS) ensure congruence.
Triangle 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?
ASA
SSS
AAS
SAS
Both triangles have side lengths of 3, 4, and 5 units (3-4-5 right triangles). Since all three pairs of corresponding sides are equal, the SSS postulate applies.
In 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?
ASA
SSS
CPCTC
AAS
Once the two triangles are shown congruent by SAS, Corresponding Parts of Congruent Triangles are Congruent (CPCTC) is used to state that the base angles are equal. CPCTC is the standard justification for corresponding parts in congruent triangles.
When 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.
True
False
In the SSA ambiguous case, if a < b but a > b·sin(C), the perpendicular dropped from the known angle creates two possible positions for the opposite vertex. This leads to two distinct triangles satisfying the given conditions.
0
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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.

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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