Question

D and E are respectively the midpoints of side BC and CA of angle ABC. Find the area of triangle BED if the area of triangle ABC is 36 cm square.

Answer 1

Hi baby

Given in ΔABC, D, E and F are midpoints of sides AB, BC and CA respectively.

BC = EC

Recall that the line joining the midpoints of two sides of a triangle is parallel to third side and half of it.

Hence DF = (1/2) BC

⇒ (DF/BC) = (1/2)  → (1)

Similarly, (DE/AC) = (1/2)  → (2)

(EF/AB) = (1/2)  → (3)

From (1), (2) and (3) we have



But if in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar

Hence ΔABC ~ ΔEDF [By SSS similarity theorem]





Hence area of ΔDEF : area of ΔABC = 1 : 4

Brainiest answer please.

Answer 2

See this

here is the answer.