45) In a right triangle, prove that the line segment joining the mid-point of the hypotenuse to the
opposite vertex is half of the hypotenuse. (4 marks)
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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
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