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.
☛ Related Questions: