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ICSE Class 9 Answered

prove that EFGH is a parallelogram
Asked by afrah.rifah | 18 Mar, 2023, 03:14: PM
answered-by-expert Expert Answer
The question must be:

ABCD is quadrilateral E,F,G and H are the midpoints of AB,BC,CD and DA respectively. Prove that EFGH is a parallelogram.

Proof:

E,F,G and H are the midpoints of AB,BC,CD and DA respectively.

In triangle ADC, 

G and H are the midpoints of sides CD and AD.

Therefore, GH || AC and GH = 1/2 AC ... By Mid-point theorem

Similarly, EF || AC and EF = 1/2 AC

So, EF = GH and EF || GH.
Thus, EFGH is a parallelogram.
Answered by Renu Varma | 20 Mar, 2023, 09:32: AM

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