Question

state and prove Pythagoras theorem​

Answer 1

$<font color= "red">$Answer:

$<font color= "</u></strong><strong><u>black</u></strong><strong><u>">$Pythagoras theorem:

$<font color= "</strong><strong>green</strong><strong>">$Step-by-step explanation:

$<font color= "</u></strong><strong><u>sky</u></strong><strong><u> </u></strong><strong><u>blue</u></strong><strong><u>">$Statement: IN A RIGHT ANGLED TRIANGLE, THE SQUARE OF THE HYPOTENUSE IS EQUAL TO THE SUM OF THE SQUARES OF THE OTHER TWO SIDES.

$<font color= "</u></strong><strong><u>black</u></strong><strong><u>">$Given: ABC is a triangle in which angle B = 90°

Construction: Draw BD perpendicular on AC from B

Proof:

Proof:In ∆ ADB and ∆ ABC

angle A = angle A [Common angle]

[Common angle]angle ADB = angle ABC [Each 90°]

∆ ADB ~ ∆ABC [A-A similarity criterion]

$<font color= "</strong><strong>orange</strong><strong>">$So,

$\frac{ad}{ab} = \frac{ab}{ac}$

=> AB²= AD×AC

Now, AB²=AD×AC ..........(1)

Similarly,

BC²=CD× AC ..........(2)

$<font color= "</strong><strong>brown</strong><strong>">$Adding equations (1) and (2) we get,

Ab²+BC² =AD × AC+CD × AC

AC=AC(AD+CD)

=AC×AC

ACtherefore AB²+BC²=AC²

$<font color= "</strong><strong>green</strong><strong>">$[hence, proved]

$<font color= "</em></strong><strong><em>blue</em></strong><strong><em>">$I hope it will helps you to guide and and and mark me brainliest ♥

Answer 2

Answer:

In Right angle triangle , the square of hypotenuse is equal to the square of sum of other two sides

Given: A right-angled triangle ABC, right-angled at B.

To Prove- AC² = AB² + BC²

Construction: Draw a perpendicular BD meeting AC at D.

Pythagoras theorem Proof

Proof:

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (corresponding sides of similar triangles)

Or, AB² = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (corresponding sides of similar triangles)

Or, BC²= CD × AC ……………………………………..(2)

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

AB²+ BC²= AD × AC + CD × AC

AB² + BC² = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC² = AB² + BC²

Hence, the Pythagorean theorem is proved.