Question

In a quadrilateral abcd, ca=cd,angle b=90°, ad^2=ab^2+ac^2prove angle acd =90

Answer 1

Answer:

Step-by-step explanation:

GIVEN: A quadrilateral ABCD , angle B = 90° And AD² = AB² + BC² + CD²

TO FIND: angle ACD

AC² = AB² + BC² ( by Pythagoras theorem)… … ..(1)

And AD² = (AB² + BC²) +CD² ( given)

=> AD² = AC² + CD² ( by 1)

So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem)

=> < ACD = 90°