Question

Given below are measurements of some parts of two triangles.Examine whether the two triangles are congruent or not,using RHS congruence rule.In case of congruent triangles, write the result in symbolic form:

△ABC has ∠B=90°,AC=8cm, AB=3cm and
△PQR has ∠P=90°,PR=3cm, QR=8cm

Answer 1

Triangles △ABC and △PQR are congruent by the RHS congruence rule because they have corresponding right angles, equal hypotenuses, and equal sides, resulting in △ABC ≅ △PQR.

Step-by-step explanation:

To determine if the two triangles are congruent using the RHS (Right angle-Hypotenuse-Side) congruence rule, we have to check if the two triangles have one right angle, one equal side that is the hypotenuse, and one equal side that is not the hypotenuse.

In △ABC, there is a right angle at B (∠B=90°), a hypotenuse AC = 8cm, and a side AB = 3cm.

Comparing it to △PQR, there is a right angle at P (∠P=90°), a hypotenuse QR = 8cm, and a side PR = 3cm.

Since both triangles have corresponding right angles, equal hypotenuses, and equal sides, we can say that the triangles are congruent by the RHS congruence rule.

Thus, the result in symbolic form is: △ABC ≅ △PQR.