Question

if in a quadrilateral ABCD angle b is equal to 90 degree and BC square is equal to C D square + a square + b square then prove that angle c d b is equal to 90 degree​

Answer 1

Question : In a quadrilateral ABCD, ∠ B = 90°, AD² = AB² + BC² + CD². Prove that ∠ACD = 90°.

Step-by-step explanation:

A quadrilateral ABCD,

∠B  =90°,

AD² = AB² + BC² + CD²

To Prove: ∠ACD = 90°

PROOF:

AD² = AB²  + BC² + CD²

AD² -  CD² = AB²  + BC² ……………(1)

In right ∆ABC,

∠B  =90°,

AC² = AB² + BC²……………….(2)

[By Pythagoras theorem]

From eq 1 & 2

AC² = AD² -  CD²

AC² + CD² = AD²

Therefore , ∠ACD = 90°

[By converse of Pythagoras theorem]

Hence, proved.

Phythagoras Theorem :

• It is known as Pythagorean' theorem .
• It is a right triangle in which the measurements for the hypotenuse, c, and another two legs a , b are given.
• It states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

${c}^{2} = {a}^{2} + {b}^{2}$