Proving Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What is the ASA (Angle-Side-Angle) congruence postulate?

Back

The ASA postulate states that 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 is the AAS (Angle-Angle-Side) congruence theorem?

Back

The AAS theorem states 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, then the triangles are congruent.

Front

What is the SAS (Side-Angle-Side) congruence postulate?

Back

The SAS postulate states that 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 is the SSS (Side-Side-Side) congruence postulate?

Back

The SSS postulate states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What does HL (Hypotenuse-Leg) mean in triangle congruence?

Back

HL is a specific case for 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

If ∆ABC≅∆XYZ, what can we conclude about the sides AB and XY?

Back

AB≅XY, meaning the lengths of sides AB and XY are equal.

Front

What is the significance of corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, which helps in proving triangle congruence.

Front

What is the relationship between the sides and angles in congruent triangles?

Back

In congruent triangles, the lengths of corresponding sides are equal, and the measures of corresponding angles are equal.

Front

How can you determine if two triangles are not congruent?

Back

If any corresponding sides or angles are not equal, the triangles are not congruent.