Ex.7.1 Q3 Congruence of Triangles - NCERT Maths Class 7

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Question

If \(ΔABC ≅ ΔFED\) under the correspondence \(ABC ↔ FED,\) write all the corresponding congruent parts of the triangles.

Text Solution

What is the known?

Two triangles which are congruent.

What is the unknown?

Triangles \(ABC\) and \(FED\) are congruent \((ΔABC ≅ ΔFED)\) under the correspondence \(ABC ↔ FED\)

Reasoning:

Two congruent triangles have exactly the same three sides and exactly the same three angles. According to the given correspondence, triangle\( ABC\) can be placed on triangle\( FED\) in such a way that \(A\) falls on \(F\), \(B\) falls on \(E\) and \(C\) falls on \(D\). So, while taking about congruence of triangles, measure of sides, measure of angles and matching of vertices are equally important.

Steps:

Given, \(ΔABC ≅ ΔFED\) under the correspondence \(ABC ↔ FED.\) The correspondence is shown with arrow in the following figure.

It is clear from the figure that

\[\begin{align}& \angle A\leftrightarrow \! \angle F,\!\angle \! B\leftrightarrow \! \angle E, \!\angle C \! \leftrightarrow \! \angle D \\& \overline{AB}\ \! \leftrightarrow \! \overline{FE}, \!\overline{BC}\ \! \leftrightarrow \! \overline{ED}, \!\overline{AC}\ \! \leftrightarrow \! \overline{FD} \\ \end{align}\]

  
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