MathIsimple

Triangle Congruence & Proofs

Master proving triangles congruent! Learn SAS, ASA, SSS, AAS, and HL criteria, and write formal geometric proofs.

9th Grade
Geometry
~60 min
🎮 Interactive Activity: Congruence Criteria Matcher

Match congruence criteria with their descriptions!

Criteria:

SAS
🎮 Interactive Activity: Proof Builder

Build a triangle congruence proof step by step!

1

Given: AB = DE, ∠A = ∠D, AC = DF

2

Triangles ABC and DEF have two sides and included angle equal

3

By SAS criterion, ΔABC ≅ ΔDEF

1. What is Congruence?

Congruent Triangles

Two triangles are congruent if all corresponding sides and angles are equal. Congruent triangles have the same size and shape.

Notation: ΔABC ≅ ΔDEF

Correspondence: A ↔ D, B ↔ E, C ↔ F

Sides: AB = DE, BC = EF, AC = DF

Angles: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F

2. SAS (Side-Angle-Side)
3. ASA (Angle-Side-Angle)
4. SSS (Side-Side-Side)
5. AAS (Angle-Angle-Side)
6. HL (Hypotenuse-Leg)
7. Writing Proofs
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What does SAS stand for?
○
2
Which criterion requires all three sides to be congruent?
○
3
If two triangles have two angles and the included side equal, they are congruent by:
○
4
What is the HL criterion used for?
○
5
If ΔABC ≅ ΔDEF, which statement is always true?
○
6
Which criterion is NOT valid for proving triangle congruence?
○
7
What does AAS require?
○
8
If two triangles are congruent, what properties are preserved?
○
9
Which information is sufficient to prove ΔABC ≅ ΔDEF by SSS?
○
10
In a proof, what is the final step after showing all criteria are met?
○