In a right triangle the square of the hypotenuse

Asked by admin @ 16/08/2021 in Math viewed by 267 People

In a right triangle, prove that the square on the hypotenuse is equal to sum of the squares on the other two sides

Answered by admin @ 16/08/2021

Figure is in the attachment

Given:

A right angled ∆ABC, right angled at B

To Prove- AC²=AB²+BC²

Construction: draw perpendicular BD onto the side AC .

Proof:

We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

We have

△ADB∼△ABC. (by AA similarity)

Therefore, AD/ AB=AB/AC

(In similar Triangles corresponding sides are proportional)

AB²=AD×AC……..(1)

Also, △BDC∼△ABC

Therefore, CD/BC=BC/AC

(in similar Triangles corresponding sides are proportional)

Or, BC²=CD×AC……..(2)

Adding the equations (1) and (2) we get,

AB²+BC²=AD×AC+CD×AC

AB²+BC²=AC(AD+CD)

( From the figure AD + CD = AC)

AB²+BC²=AC . AC

Therefore, AC²=AB²+BC²

This theroem is known as Pythagoras theroem...

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Hope this will help you.....

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. find the area of the triangle. b = 2 in.; c = 6 in. a = sq. in.

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 334 persons

Which of the following states the pythagorean theorem? a. in a right triangle, the hypotenuse equals the sum of the squares of the legs. b. in a right triangle, the square of the hypotenuse equals the sum of the legs. c. in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. d. in a right triangle, the hypotenuse equals the sum of the legs.

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 558 persons

A parallelogram has coordinates of (5, 17), (10, 20), (18, 9), and (13, 6). which right triangle represents one of the cutouts from the box method?

Asked by suad2254 @ 02/06/2022 in Mathematics viewed by 380 persons

In a right triangle the square of the hypotenuse

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