Triangle Congruence Concepts

Front

What does the acronym SAS stand for in triangle congruence?

Back

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

Front

What does the acronym AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a rule 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, then the triangles are congruent.

Front

What does the acronym ASA stand for in triangle congruence?

Back

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

Front

What does the acronym SSS stand for in triangle congruence?

Back

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

Front

What does the acronym HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a rule 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, then the triangles are congruent.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

How can you determine if two triangles are not congruent?

Back

Two triangles are not congruent if their corresponding sides and angles do not match in size and measure.

Front

Provide an example of using the AAS rule to prove triangle congruence.

Back

If triangle ABC has angles A = 50° and B = 60°, and side AC = 5 cm, and triangle DEF has angles D = 50° and E = 60°, and side DF = 5 cm, then triangles ABC and DEF are congruent by AAS.

Front

Provide an example of using the SAS rule to prove triangle congruence.

Back

If triangle XYZ has side XY = 7 cm, angle Y = 45°, and side YZ = 5 cm, and triangle PQR has side PQ = 7 cm, angle Q = 45°, and side QR = 5 cm, then triangles XYZ and PQR are congruent by SAS.

Front

What is the significance of the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem is significant because it provides a quick way to prove the congruence of right triangles using only the hypotenuse and one leg.