Question

IN TRIANGLE ABC,ANGKE ACB = 90. M IS THE MIDPOINT OF HYPOTENUSE AB. PROVE THAT CM =1/2AB.
GUYS PLZ HELP ME WID THIS QUESTION.....

Answer 1

If angle ACB is a right angle, then in triangle ABC join M to C and construct a line through AC parallel to BC meeting AC at D.
Now, angle ADM=angle ACB.
In triangle ADM and triangle DCM
DM=DM(common)
Angle ADM=angle ACB= 90(proved above)
AD=CD(mid point theorem)
Triangle ADM is congruent with triangle DCM
AM= CM(cpct)
Also, as M is the mid point,
AM=1/2 AB
Therefore, CM=1/2 AB
Hence proved

Answer 2

very easy ok
lets solve


sorry for late but finally solved

thanks