Question

state and prove Pythagoras theorem​

Answer 1

Step-by-step explanation:

statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: ABC is a triangle in which ∠ABC=90

∘

Construction: Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A [Common angle]

∠ADB=∠ABC [Each 90

∘

]

△ADB∼△ABC [A−A Criteria]

So,

AB

AD

=

AC

AB

Now, AB

2

=AD×AC ..........(1)

Similarly,

BC

2

=CD×AC ..........(2)

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

AB

2

+BC

2

=AD×AC+CD×AC

=AC(AD+CD)

=AC×AC

∴AB

2

+BC

2

=AC

2

[henceproved]

solution

Answer 2

Answer:

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

Step-by-explaination:

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.