Question

Solve the following questions.

Answer 1

Here is your answer user.

Here Pythagorean theorems.

Construction:-

Join angle B to Base AC perpendicular.

proof :-

In ∆CDB and ∆CBA.

angle C = angle C

angle B = angle D

°•° by AA properties ∆CDB ~ ∆CBA.

DC/BC = BC/AC

BC² = DC * AC -------- (1)

Again,

In ∆ADB and ∆ABC

angle A = angle A (common)

angle D = angle B (90°)

By "AA" properties ∆ADB ~ ∆ABC.

AD/AB = AB/AC.

AB² = AD*AC.

Adding equation (1) and (2) we get,

AB² + BC² = AD * AC + DC*AC

= AC (AD+DC)

= AC(AC)

= AC²

Hence proved,

AB²+BC² = AC²

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