Exercise 9A: Congruence of Triangles

In this exercise, we will explore the concept of congruence of triangles. Congruent triangles are those which have the same shape and size. When two triangles are congruent, all corresponding sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.

Key Concepts:
1. Congruence: Two objects are said to be congruent if they have the same shape and size.
2. Congruent Triangles: Two triangles are congruent if their corresponding sides and angles are equal.
3. Criteria for Congruence: There are various criteria for proving the congruence of triangles, including SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), RHS (Right Angle-Hypotenuse-Side), and AAS (Angle-Angle-Side).

SSS (Side-Side-Side) Congruence:
If three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.

SAS (Side-Angle-Side) Congruence:
If two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.

ASA (Angle-Side-Angle) Congruence:
If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the triangles are congruent.

RHS (Right Angle-Hypotenuse-Side) Congruence:
If the hypotenuse and one side of a right-angled triangle are equal to the corresponding hypotenuse and side of another right-angled triangle, then the triangles are congruent.

AAS (Angle-Angle-Side) Congruence:
If two angles and a non-included side of one triangle are equal to the corresponding two angles and the non-included side of another triangle, then the triangles are congruent.

Example Problems:
1. Given that AB = XY, BC = YZ, and ∠ABC = ∠XYZ, prove that ΔABC ≅ ΔXYZ using the SAS criterion.
2. In ΔPQR, PR = 10 cm, QR = 6 cm, and m∠P = 60°. In ΔSTU, TU = 10 cm, US = 6 cm, and m∠S = 60°. Prove that ΔPQR ≅ ΔSTU using the SAS criterion.

Remember to carefully apply the appropriate congruence criterion and provide step-by-step explanations for each problem.

9 A is the chapter of construction not congruency