Ex.7.2 Q10 Congruence of Triangles - NCERT Maths Class 7

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Question

 Explain, why

\(ΔABC ≅ ΔFED\).

Text Solution

 

What is known?

Two right angles triangles \(ΔABC\) and \(ΔFED\) in which one side and one angle are equal.

What is unknown?

Why \(ΔABC ≅ ΔFED\)?

Reasoning:

This question is based on congruence of a right-angled triangle. In this question, one angle and a side of a right-angled triangle are equal to the corresponding one angle and a side of another right-angled triangle. Now, by using congruence based on right-angled triangle, you can find the reason why these two triangles are congruent.

Steps:

Given,

In triangles, \(ABC\) and \(FED\),

\[\begin{align}\angle \text{A}\,&=\ \angle \,\text{F}\\ \angle \text{B}\,&=\,\,\angle \text{E=9}{{\text{0}}^{\circ }}\\\rm{} BC &= ED\end{align}\]

Therefore, \(ΔABC ≅ ΔFED\) (By \(RHS\) congruence rule)