Understanding Triangle Congruency

Front

What is triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

List the criteria for triangle congruence.

Back

The criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which is a criterion that states 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 is a criterion that states 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 is a criterion that states 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 is a criterion that states 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 is a criterion that applies to right triangles, stating 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

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length, which also means the angles opposite those sides are equal.

Front

If two triangles are congruent, what can be said about their corresponding angles and sides?

Back

If two triangles are congruent, their corresponding angles are equal, and their corresponding sides are equal in length.

Front

What is the significance of the SSA condition in triangle congruence?

Back

The SSA condition (Side-Side-Angle) is not a valid criterion for triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.