#
ABC is a right angled triangle, right angled at B. D and E are any points on AB and BC. Prove that

1
Log in to add a comment

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

We can prove this by using Pythagoras theorem. At B we have a right angle.

In the triangle, ABE, we get: AE² = AB² + BE²

In the triangle DBC, we get : CD² = DB² + BC²

adding the above two equations. we get:

AE² + CD² = (AB² + BC²) +( DB² + BE²)

= AC² + DE²

This equation will be true for a quadrilateral with two adjacent sides being perpendicular.

In the triangle, ABE, we get: AE² = AB² + BE²

In the triangle DBC, we get : CD² = DB² + BC²

adding the above two equations. we get:

AE² + CD² = (AB² + BC²) +( DB² + BE²)

= AC² + DE²

This equation will be true for a quadrilateral with two adjacent sides being perpendicular.