What does it mean for two triangles to be congruent?

Two triangles are congruent if all their corresponding sides and corresponding angles have the same measure.

State the Side-Side-Side (SSS) Triangle Congruence Theorem in your own words.

If all three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.

In ASA, the congruent side is located between the two congruent angles. In AAS, the congruent side is not between the two congruent angles.

Grade 10th Grade · Math · 45 min

I can prove triangle congruence using SSS, SAS, ASA, and AAS.

Mashup Math · 7:25

Triangle Congruence Theorems Explained: ASA, AAS, HL

3 key concepts

1
The five triangle congruence theorems are: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).
2
The Side-Angle-Side (SAS) theorem requires that the congruent angle be in between the two congruent sides.
3
The Angle-Angle-Side (AAS) Theorem differs from Angle-Side-Angle (ASA) because the congruent angles are consecutive, meaning one after the other, with the congruent side next to them, not in between.

9 questions · Multiple choice & Short answer

Quick comprehension check

“Triangles ABC and XYZ have AB ≅ XY, BC ≅ YZ, and CA ≅ ZX. Which congruence theorem proves that ΔABC ≅ ΔXYZ?”

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