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CBSE Class 10 Answered

ABCD is a parallelogram and E,G,H and F are the mid points of the sides AB, BC, CD, DA. Prove that =
Asked by Topperlearning User | 03 Oct, 2017, 01:45: PM
answered-by-expert Expert Answer

We see that  AB = CD (opposite sides of a parallelogram are equal)

begin mathsize 12px style 1 half AB space equals space 1 half CD space rightwards double arrow space AE space equals space CH end style 

Similarly AF = GC

Also (opposite angles of a parallelogram are equal)

 (SAS rule)

This is also a special case of similarity where the ratio of corresponding sides is 1:1

begin mathsize 12px style fraction numerator straight A open parentheses increment AEF close parentheses over denominator straight A open parentheses increment GCH close parentheses end fraction equals EF squared over GH squared equals 1 end style

Hence area of triangles AEF and GCH are equal.

Answered by | 03 Oct, 2017, 03:45: PM

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