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# In each of the given pairs of triangles of Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:

**Solution:**

Given, the figure represents two triangles ABC and CDE.

We have to apply the RHS congruence criterion to the triangle.

We have to write the __congruent triangles__ in symbolic form.

RHS congruence theorem states that, if the hypotenuse and side of one __right-angled triangle__ are equal to the __hypotenuse__ and the __corresponding side__ of another right-angled triangle, the two triangles are congruent.

Considering __triangle__ ABC,

By Pythagorean theorem,

AC² = AB² + BC²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

Taking __square root__,

AC = 10 cm

Considering triangle CDE,

BD = BC + CD

14 = 8 + CD

CD = 14 - 8

CD = 6 cm

By Pythagorean theorem,

EC² = CD² + DE²

10² = 6² + DE²

100 = 36 + DE²

DE² = 100 - 36

DE² = 64

Taking square root,

DE = 8 cm

Considering triangle ABC and CDE,

AC and EC are the hypotenuse of the triangle ABC and CDE.

AC = EC = 10 cm

Also, BC = DE = 8 cm

∠ABC = ∠CDE = 90°

By RHS rule, ∆ABC ≅ ∆CDE

**✦ Try This: **In each of the given pairs of triangles of Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 6

**NCERT Exemplar Class 7 Maths Chapter 6 Problem 135 (d)**

## In each of the given pairs of triangles of ABCDE Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:

**Summary:**

The given pair of triangles are congruent by RHS congruence criterion. The symbolic form is ∆ABC ≅ ∆CDE.

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