# Ex.7.2 Q7 Congruence of Triangles - NCERT Maths Class 7

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## Question

In a squared sheet, draw two triangles of equal areas such that

(i) the triangles are congruent.

(ii) the triangles are not congruent.

What can you say about their perimeters?

## Text Solution

Steps:

Draw two triangles of equal areas,

(i)

Triangles $$ABC$$ and $$XYZ$$ have the same area and are congruent to each other. Also, perimeter of both the triangles will be equal.

Such that,  $$\overline{AB}\text{ }=\text{ }\overline{DE},\overline{BC}\text{ }=\text{ }\overline{EF}\;\rm{and}\;\overline{AC}\text{ }=\text{ }\overline{DF}$$
On adding, we get $$\overline{AB}+\overline{BC}+\overline{AC}=\overline{DE}+\overline{EF}+\overline{DF}$$
i.e, perimeter of both the triangles are equal.

(ii)

Here, we have drawn two triangles $$ABC$$ and $$PQR$$ which are not congruent to each other.
Such that ,$$\overline{AB}\text{ }\ne \text{ }\overline{XY},\overline{BC}\text{ }\ne \text{ }\overline{YZ}\;\rm{and}\;\overline{AC}\text{ }\ne \text{ }\overline{XZ}$$
On adding, we get $$\overline{AB}+\overline{BC}+\overline{AC}=\overline{XY}+\overline{YZ}+\overline{XZ}$$
Also, the perimeter of both the triangles will not be the same.

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