Question

ABC is a triangle right angle at B and P is mid point of AC prove that PB=PA=1/2AC​

Answer 1

MATHS

In the adjoining figure, △ABC is right-angled at B and P is the mid-point of AC, show that, PA=PB=PC.

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ANSWER

GIVEN QP∣∣BC

consider triangles AQP,ABC

angle A= angle A

angle AQP= angle ABC

angle APQ=angle ACB

therefore triangles ABC and AQP are similar

but AP=PC

therefore AP:AC=1:2

therefore AQ:AB=1:2

therefore Q is mid point of AB

now consider triangles AQP,BQP

AQ=BQ

QP=QP

angle AQP=angle BQP

according to SAS axiom AQP congruent to BQP

therefore PA=PB

therefore PA=PB=PC