Proving Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate 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 ASA stand for in triangle congruence?

Back

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

Back

AAS stands for Angle-Angle-Side, a postulate 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 HypLeg stand for in triangle congruence?

Back

HypLeg stands for Hypotenuse-Leg, a postulate used for right triangles that states 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 significance of vertical angles in triangle congruence?

Back

Vertical angles are always congruent, which can be used to establish congruence between triangles when proving them.

Front

What is the Reflexive Property in triangle congruence?

Back

The Reflexive Property states that a geometric figure is congruent to itself, which can be used to show that a side or angle is shared between two triangles.

Front

When is it 'not possible' to prove triangle congruence?

Back

It is 'not possible' to prove triangle congruence when there is insufficient information or when the given information does not meet any of the congruence postulates.

Front

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

Back

If triangle ABC has AB = 5 cm, AC = 7 cm, and angle A = 60 degrees, and triangle DEF has DE = 5 cm, DF = 7 cm, and angle D = 60 degrees, then triangles ABC and DEF are congruent by SAS.

Front

Provide an example of using the ASA postulate to prove triangle congruence.

Back

If triangle GHI has angle G = 45 degrees, angle H = 60 degrees, and side GH = 8 cm, and triangle JKL has angle J = 45 degrees, angle K = 60 degrees, and side JK = 8 cm, then triangles GHI and JKL are congruent by ASA.