Question

triangle ABC is a triangle right angled at B; and P is the mid point of AC.Prove that. i)PQ perpendicular at AB ii)Q is the mid point of AB iii)PB=PA=1/2AC(half AC)​

Answer 1

Step-by-step explanation:

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

Answered By yadavjii64