Ex 7.2, 7 In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. What can you say about their perimeters?Two congruent triangles
Here,
∆ABC ≅ ∆DEF
Finding ar (ABC)
∴ ar (ABC) = 2 + 2
= 4 square units
Finding ar (DEF)
∴ ar (DEF) = 2 + 2
= 4 square units
∴ ar (ABC) = ar (DEF)
Thus, triangles are of equal areas and are congruent
Now,
Let’s check perimeter of both triangles
As Δ ABC ≅ Δ DEF
By CPCT
AB = DE
BC = EF
AC = DF
Adding (1), (2) & (3)
AB + BC + AC = DE + EF + DF
Perimeter of Δ ABC = Perimeter of Δ DEF
Thus, perimeters of congruent triangles are also equal
Ex 7.2, 7 In a squared sheet, draw two triangles of equal areas such that (ii) the triangles are not congruent. What can you say about their perimeters?
Two triangles not congruent
Here,
∆MNO ≇ ∆IJK
Finding ar (MNO)
∴ ar (MNO) = 2 + 2
= 4 square units
Finding ar (IJK)
∴ ar (IJK) = 2 + 2
= 4 square units
Thus,
ar (MNO) = ar (IJK)
But ∆MNO ≇ ∆IJK
Measuring Perimeter
By measuring Perimeter,
Perimeter of MNO > Perimeter of IJK
So, Perimeter are not equal.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.