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?
Solution:
(i) If two triangles are congruent, then all the corresponding parts of the triangles will be equal.
Let us consider two triangles, ΔABC and ΔDEF
On the given square sheet, we have drawn two congruent triangles.
such that, ∆ ABC ≅ ∆ DEF
We can say that,
AB = DE,
BC = EF
AC = DF
On adding the three relations a bove, we get
AB + BC + AC = DE + EF + DF
Thus, Perimeter of ∆ ABC = Perimeter of ∆ DEF
(ii) In this case, we have drawn two triangles ABC and PQR which are not congruent.
Such that
Adding the given relations, we get
AB + BC + AC ≠ PQ + QR + PR
Thus, Perimeter of ∆ ABC ≠ Perimeter of ∆ PQR.
From the above, we can say that if two triangles are not congruent then the perimeter is also not equal and if they are congruent then their perimeters are also equal.
☛ Check: NCERT Solutions Class 7 Maths Chapter 7
Video Solution:
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?
Class 7 Maths NCERT Solutions Chapter 7 Exercise 7.2 Question 7
Summary:
In a squared sheet, we have drawn two triangles of equal areas such that (i) The triangles are congruent. (ii) The triangles are not congruent. We can say that if two triangles are not congruent then the perimeter is also not equal and if they are congruent then their perimeters are also equal.
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