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Triangle Congruence Practice

Quiz

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.SRT.B.5, HSG.CO.C.9

Standards-aligned

Nicole Marsula

Used 55+ times

FREE Resource

About this resource

This quiz focuses on triangle congruence theorems, which is a fundamental topic in high school geometry typically taught at the 9th grade level. Students need to master the five valid triangle congruence theorems: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles only). The questions require students to analyze given triangles with marked congruent parts and determine which theorem applies, while also recognizing invalid theorems like AAA and SSA that cannot prove congruence. Students must understand key geometric concepts including shared sides, vertical angles, angle bisectors, midpoints, and the Reflexive Property. The quiz also introduces CPCTC (Corresponding Parts of Congruent Triangles are Congruent), which is essential for proving specific parts congruent after establishing triangle congruence through formal geometric proofs. Created by Nicole Marsula, a Mathematics teacher in US who teaches grade 9. This practice quiz serves multiple instructional purposes throughout the geometry unit on triangle congruence. Teachers can use it as a warm-up activity to activate prior knowledge before introducing new proof techniques, or as guided practice during initial instruction to help students distinguish between valid and invalid congruence theorems. The quiz works exceptionally well for homework assignments, allowing students to practice identifying congruence theorems independently, and as formative assessment to gauge student understanding before moving to more complex proof writing. The inclusion of common misconceptions like AAA and SSA makes this particularly valuable for review sessions before unit tests. This content aligns with Common Core standards G.CO.7 and G.CO.8, which require students to use the definition of congruence in terms of rigid motions and prove geometric theorems involving triangle congruence.

14 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which Triangle Congruence Theorem proves these triangles congruent?

AAS

ASA

SAS

HL

Cannot be proven congruent

Answer explanation

These triangles are congruent by ASA.
Angle-Side-Angle

Tags

CCSS.HSG.SRT.B.5

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which Triangle Congruence Theorem proves these triangles congruent?

AAS

ASA

SAS

SSS

Cannot be proven congruent

Answer explanation

Mark the shared side as congruent. Then we can see the triangles are congruent by SSS.
Side-Side-Side

Tags

CCSS.HSG.SRT.B.5

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which Triangle Congruence Theorem proves these triangles congruent?

AAS

ASA

SSA

HL

Cannot be proven congruent

Answer explanation

First, mark the vertical angles as congruent.
-------------
Then, focus on one triangle and see Angle-Angle-Side.
AAS
This is not ASA because the Side is NOT between the angles.

Tags

CCSS.HSG.SRT.B.5

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which Triangle Congruence Theorem proves these triangles congruent?

AAS

SAS

ASA

SSS

Answer explanation

First, mark the shared side as congruent.
Then, focus on just one of the triangles if you need to.
These triangles are congruent by Angle-Side-Angle.
ASA

Tags

CCSS.HSG.SRT.B.5

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which Triangle Congruence Theorem proves these triangles congruent?

AAA

ASA

AAS

Cannot be proved congruent!

Answer explanation

Even though all the angles are marked congruent, AAA, Angle-Angle-Angle is NOT a triangle congruence theorem.
This cannot prove triangles are congruent.
Remember "No screaming! AAA!!!"

Tags

CCSS.HSG.SRT.B.5

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

For which situation could you prove
∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem?

Answer explanation

The hypotenuses are only marked as congruent in the third picture.

Tags

CCSS.HSG.SRT.B.5

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

How are the triangles congruent?

SAS

SSA

ASA

These are not congruent

Answer explanation

Even though both triangles have two sides and one angle marked congruent, they are not in the same order.
SAS is not congruent to SSA, so these triangles cannot be proven congruent.

Tags

CCSS.HSG.SRT.B.5

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Triangle Congruence Practice

14 questions

Which Triangle Congruence Theorem proves these triangles congruent?

These triangles are congruent by ASA.
Angle-Side-Angle

Which Triangle Congruence Theorem proves these triangles congruent?

Mark the shared side as congruent. Then we can see the triangles are congruent by SSS.
Side-Side-Side

Which Triangle Congruence Theorem proves these triangles congruent?

First, mark the vertical angles as congruent.
-------------
Then, focus on one triangle and see Angle-Angle-Side.
AAS
This is not ASA because the Side is NOT between the angles.

Which Triangle Congruence Theorem proves these triangles congruent?

First, mark the shared side as congruent.
Then, focus on just one of the triangles if you need to.
These triangles are congruent by Angle-Side-Angle.
ASA

Which Triangle Congruence Theorem proves these triangles congruent?

Even though all the angles are marked congruent, AAA, Angle-Angle-Angle is NOT a triangle congruence theorem.
This cannot prove triangles are congruent.
Remember "No screaming! AAA!!!"

For which situation could you prove
∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem?

The hypotenuses are only marked as congruent in the third picture.

How are the triangles congruent?

Even though both triangles have two sides and one angle marked congruent, they are not in the same order.
SAS is not congruent to SSA, so these triangles cannot be proven congruent.

Are these triangles congruent?

Once we mark the shared side as a congruent leg, we can see they are congruent by HL (Hypotenuse-Leg).

Are these triangles congruent?

Even though Side-Side-Angle are marked congruent, SSA is NOT a triangle congruence theorem.
This cannot prove triangles are congruent.
Remember "No swearing!"

Are the triangles congruent?

Since the second triangle does not have the third side marked as a congruent pair, we can only use SAS.
Side-Angle-Side

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Triangle Congruence Practice

14 questions

Which Triangle Congruence Theorem proves these triangles congruent?

These triangles are congruent by ASA.Angle-Side-Angle

Which Triangle Congruence Theorem proves these triangles congruent?

Mark the shared side as congruent. Then we can see the triangles are congruent by SSS.Side-Side-Side

Which Triangle Congruence Theorem proves these triangles congruent?

First, mark the vertical angles as congruent.-------------Then, focus on one triangle and see Angle-Angle-Side.AASThis is not ASA because the Side is NOT between the angles.

Which Triangle Congruence Theorem proves these triangles congruent?

First, mark the shared side as congruent.Then, focus on just one of the triangles if you need to.These triangles are congruent by Angle-Side-Angle.ASA

Which Triangle Congruence Theorem proves these triangles congruent?

Even though all the angles are marked congruent, AAA, Angle-Angle-Angle is NOT a triangle congruence theorem.This cannot prove triangles are congruent.Remember "No screaming! AAA!!!"

For which situation could you prove ∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem?

The hypotenuses are only marked as congruent in the third picture.

How are the triangles congruent?

Even though both triangles have two sides and one angle marked congruent, they are not in the same order.SAS is not congruent to SSA, so these triangles cannot be proven congruent.

Are these triangles congruent?

Once we mark the shared side as a congruent leg, we can see they are congruent by HL (Hypotenuse-Leg).

Are these triangles congruent?

Even though Side-Side-Angle are marked congruent, SSA is NOT a triangle congruence theorem.This cannot prove triangles are congruent.Remember "No swearing!"

Are the triangles congruent?

Since the second triangle does not have the third side marked as a congruent pair, we can only use SAS.Side-Angle-Side

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These triangles are congruent by ASA.
Angle-Side-Angle

Mark the shared side as congruent. Then we can see the triangles are congruent by SSS.
Side-Side-Side

First, mark the vertical angles as congruent.
-------------
Then, focus on one triangle and see Angle-Angle-Side.
AAS
This is not ASA because the Side is NOT between the angles.

First, mark the shared side as congruent.
Then, focus on just one of the triangles if you need to.
These triangles are congruent by Angle-Side-Angle.
ASA

Even though all the angles are marked congruent, AAA, Angle-Angle-Angle is NOT a triangle congruence theorem.
This cannot prove triangles are congruent.
Remember "No screaming! AAA!!!"

For which situation could you prove
∆1 ≅ ∆2 using the HL (Hypotenuse-Leg) Theorem?

Even though both triangles have two sides and one angle marked congruent, they are not in the same order.
SAS is not congruent to SSA, so these triangles cannot be proven congruent.

Even though Side-Side-Angle are marked congruent, SSA is NOT a triangle congruence theorem.
This cannot prove triangles are congruent.
Remember "No swearing!"

Since the second triangle does not have the third side marked as a congruent pair, we can only use SAS.
Side-Angle-Side