Question

in a right triangle prove that the line segment joining the mid point of hypotenuse to the opposite vertex is half the hypotenuse
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Answer 1

Step-by-step explanation:

Let P be the mid point of the hypotenuse of the right △ABC right angled at B

Draw a line parallel to BC from P meeting B at O

Join PB

In △PAD and △PBD

∠PDA=∠PDB90

∘

each due to conv of mid point theorem

PD=PD ....... (common)

AD=DB ...... (As D is mid point of AB)

So △ PAD and PBD are congruent by SAS rule

PA=PB ...... (C.P.C.T)

As PA=PC .... (Given as P is mid-point)

∴PA=PC=PB

Answer 2

Answer:

Step-by-step explanation:

Let P be the mid point of the hypotenuse of the right △ABC right angled at B

Draw a line parallel to BC from P meeting B at O

Join PB

In △PAD and △PBD

∠PDA=∠PDB=90

∘

each due to conv of mid point theorem

PD=PD  (common)

AD=DB  (As D is mid point of AB)

So △ PAD and PBD are congruent by SAS rule

PA=PB  (C.P.C.T)

As PA=PC  (Given as P is mid-point)

∴PA=PC=PB