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ABC is a triangle right angled at C. A line through mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

(i) D is mid-point of AC

(ii) MD AC

(iii) CM = MA = AB

Asked by Topperlearning User 10th December 2013, 1:48 AM
Answered by Expert
Answer:

(i) AM = BM, MD||BC (given)

AD = CD (Mid-point theorem)

Hence, D is mid-point of AC.

(ii) 1 = 2 = 90o (Corresponding angles)

MD AC

(iii) ADM = MDC = 90o

AD = CD

MD = MD

(by SAS)

CM = AM

But AM =

Hence, CM = AM =

Answered by Expert 10th December 2013, 3:48 AM
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