#5.2 Congruent Polygons

Front

What does it mean for two polygons to be congruent?

Back

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

Front

If ΔABC ≅ ΔXYZ, what can we say about the corresponding sides and angles?

Back

The corresponding sides and angles of the two triangles are equal: AB = XY, BC = YZ, AC = XZ and ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.

Front

What is the significance of the order of vertices in congruence statements?

Back

The order of vertices in congruence statements indicates which angles and sides correspond to each other. For example, in ΔABC ≅ ΔXYZ, A corresponds to X, B to Y, and C to Z.

Front

What is the Side-Angle-Side (SAS) Congruence Postulate?

Back

The SAS Congruence 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 two triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) Congruence Postulate?

Back

The ASA Congruence 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 two triangles are congruent.

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

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

Front

How can you prove that two polygons are congruent?

Back

To prove that two polygons are congruent, you can show that their corresponding sides and angles are equal using congruence postulates or theorems.

Front

What is the difference between congruence and similarity in polygons?

Back

Congruent polygons are identical in shape and size, while similar polygons have the same shape but may differ in size (corresponding sides are proportional).

Front

What does the notation ΔABC ≅ ΔXYZ indicate?

Back

The notation ΔABC ≅ ΔXYZ indicates that triangle ABC is congruent to triangle XYZ, meaning their corresponding sides and angles are equal.

Front

What is the importance of corresponding parts in congruent triangles?

Back

Corresponding parts in congruent triangles are important because they allow us to establish relationships between the triangles, such as equal lengths and angles, which can be used in proofs and problem-solving.