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

## 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.