Congruent Triangle Theorems

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 congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What is the significance of congruence statements like ∆EHG≅∆KFC?

Back

Congruence statements indicate that two triangles are congruent, meaning all corresponding sides and angles are equal.

Front

What is the difference between ASA and AAS?

Back

ASA (Angle-Side-Angle) requires the included side to be congruent, while AAS (Angle-Angle-Side) does not require the side to be between the two angles.

Front

Can triangles be congruent if they have the same angles but different side lengths?

Back

No, triangles cannot be congruent if they have the same angles but different side lengths; this is known as the AAA (Angle-Angle-Angle) condition, which does not guarantee congruence.

Front

What is the purpose of a congruence statement?

Back

A congruence statement is used to express that two geometric figures are congruent, allowing for the comparison of their corresponding parts.

Front

What does the term 'congruent' mean in geometry?

Back

In geometry, 'congruent' means that two figures have the same shape and size, with corresponding sides and angles being equal.

Front

What is the importance of the included angle in the ASA postulate?

Back

The included angle in the ASA postulate is crucial because it ensures that the two angles and the side between them create a unique triangle configuration.

Front

How can you determine if two triangles are congruent using the SSS postulate?

Back

To determine if two triangles are congruent using the SSS postulate, measure all three sides of each triangle and check if they are equal.

Front

What is a counterexample to the claim that AAA implies congruence?

Back

A counterexample to AAA implying congruence is two triangles that are similar but not congruent, such as a small triangle and a larger triangle with the same angles.