4.6 Solving with Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

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

Front

If ∆ABC ≅ ∆LMN, what can we say about the corresponding sides?

Back

The corresponding sides are equal: AB ≅ LM, BC ≅ MN, AC ≅ LN.

Front

What is the Congruence Postulate for triangles?

Back

The Congruence Postulates (SSS, SAS, ASA, AAS, and HL) provide criteria to determine if two triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, which applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

If ∠C = 40° in congruent triangles, what can we say about the corresponding angle in the other triangle?

Back

The corresponding angle in the other triangle is also 40°, since corresponding angles in congruent triangles are equal.

Front

If BC = 15 in triangle ∆ABC and ∆XYZ is congruent to ∆ABC, what is the length of XY?

Back

XY = 15, since corresponding sides in congruent triangles are equal.