Question

prove that in a right angle triangle the median of the hypotenuse from the angle containing right angle is half the hypotenuse

Answer 1

Hey there !

Given : ABC right angled at C. M is the mid-point of AB. 

Construction : join M to mid-point of AC which is D. 

To prove: CM = MA
 
Proof : In triangle ABC , D and M are the mid-points of sides AD and AB respectively. 

So by mid-point theorem ,

DM||CB ,

=> angle ADM = angle ACB ( corresponding angles ) 

=> angle ADM = 90° 

Now , 

angle ADM + angle CDM = 180°(linear pair ) 

=> 90° + angle CDM =180° 

=> angle CDM = 90° 

In ADM and CDM, 

AD = DC ( since D is the midpoint of AC )

angle ADM = angle CDM ( each 90°) 

DM = MD ( common ) 

So , by SAS rule , CDM is congruent to ADM 

=> CM=MA ( by c.p.c.t. )

Hope it helps !!!

be brainly , together we go far ♥