Proving Triangles Congruent

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is being compared to triangle ABC, they are congruent by the Reflexive Property.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a criterion for triangle congruence that applies to right triangles. 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 does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence stating 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 ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence stating that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, the triangles are congruent.

Front

What is the significance of Vertical Angles in triangle congruence?

Back

Vertical Angles are always congruent. If two triangles share a pair of vertical angles, this can help establish congruence using the AAS or ASA criteria.

Front

What is the difference between congruent triangles and similar triangles?

Back

Congruent triangles have the same size and shape, meaning all corresponding sides and angles are equal. Similar triangles have the same shape but not necessarily the same size; their corresponding angles are equal, and their sides are proportional.

Front

How can you prove triangles are congruent using the SAS criterion?

Back

To prove triangles are congruent using the SAS criterion, you need to show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What additional information is needed to prove triangles congruent by SSS?

Back

To prove triangles congruent by SSS, you need to know the lengths of all three sides of both triangles.

Front

What additional information is needed to prove triangles congruent by HL?

Back

To prove triangles congruent by HL, you need to know the lengths of the hypotenuse and one leg of both right triangles.