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Question

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallels to BC intersect AC at D. Show that CM=MA=12AB

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Solution

To show : CM=MA=12AB

In AMD and CMD

AD=DC (D is midpoint)

ADM=CDM

DM=DM (common)

AMD=CMD (SAS congruence rule )

AM=CM(CPCT)(1)

AM=12AB(M is midpoint)(2)

from eq (1) and (2)

CM=AM=12AB

1347732_1232255_ans_d4d27a23536c44d4bc040f8d0a6de61b.PNG

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