Question

1.All congruent triangles are equal in area but the triangles equal in area need not be

congruent. (True/False)​

Answer 1

Answer:

true.............

......

Answer 2

It's true that all congruent triangles have equal areas but vice- a- versa may not always be true.

Explanation:

• Two or more triangles are said to be congruent if they are equal in shape and size.
• Hence, congruent triangles have all of their corresponding pairs of sides and angles equal.
• Hence if two triangles ABC and PQR with side length a, b, c and p, q, r and angles A, B, C and P, Q, R are said to be congruent then $a=p,\ b=q,\ c=r\ and\ \angle A=\angle P,\ \angle B=\angle Q,\ \angle C=\angle R$
• Since the area of a triangle is given by $\frac{1}{2}\ x \ base\ x\ height$ congruent triangles having the same dimensions have equal area.
• But the different combinations of base and height can give the product value.
• Therefore, not all triangles having same area have the same dimensions. Hence, the statement is true.