Question

Triangle ABC IS ISOCELES WITH AC=BC D IS THE MID POINT OF AB PROVE THAT CD IS PERPENDICULAR TO AB​

Answer 1

Answer:

This can be done by SAS Congruency

Step-by-step explanation:

Given ∆ABC is isosceles so, AC=AB and AD=DB

TO PROVE: CD perpendicular to AB

PROOF:-

IN ∆ACD & ∆ACB

AC=AB (given)

AD=BD(GIVEN)

<A= <C ( opposite angles of isosceles triangle)

So, ∆ACD IS CONGRUENT TO ∆BCD (By SAS)

so, <ADC= <BDC ( CPCT)

since <ADC+<BDC=180° (LINEAR PAIR)

<ADC+<ADC=180° (<ADC=<BDC)

2<ADC= 180°

<ADC=90°

Hence AD IS perpendicual to AB