Congruent Triangles

Front

What is a congruent triangle?

Back

A triangle that has the same size and shape as another triangle. This means all corresponding sides and angles are equal.

Front

What does SAS stand for in triangle congruence?

Back

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 SSS stand for in triangle congruence?

Back

Side-Side-Side: A postulate 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 ASA stand for in triangle congruence?

Back

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

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 is the significance of the included angle in SAS?

Back

The included angle is the angle formed between the two sides being compared. It is crucial for proving congruence using the SAS postulate.

Front

Can two triangles be congruent if only two sides are equal?

Back

No, two triangles cannot be proven congruent with only two sides equal unless the included angle is also known (SAS).

Front

What is the difference between SSA and other congruence postulates?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

If ∆ABC≅∆XYZ, what can be inferred about their corresponding sides?

Back

AB≅XY, BC≅YZ, AC≅XZ.

Front

What is the relationship between corresponding angles in congruent triangles?

Back

If two triangles are congruent, then all corresponding angles are equal.