Triangle Congruence Practice
Authored by Nicole Marsula
Mathematics
9th Grade
CCSS covered
Used 76+ times
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About
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.
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14 questions
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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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