Question

state and prove Converse of Pythagoras theorem​

Answer 1

Answer:

the Converse of pGt ther`n

if

• a2 +b2 =c2 holds

than

• DABC is right angled triangle with angle at c

How to prove that Converse of pGt theorem ?

now construct another tringle withe follow

• EF= BC=a
• DF is a right angle.
• FD =CA=b

• in DDFE
• by pGt theo`n
• DF = √a2+√b2....... in equation (2)
• by 1 the given

AB = C =√a2 +√b2

Therefore...AB = DE

by the construction BC =EF

and CA = FD

D ABC © D DEF (sss)

I am sorry to not drawing the figer

Answer 2

Step-by-step explanation:

Statement:

In a Triangle the square of longer side is equal to the sum of squares of the other two sides, then the triangle is a right angled triangle.

Given -

A Triangle ABC such that

BC² = AB² + AC²

To Prove -

Angle A = 90°

Construction -

Draw a ∆DEF such that AB = DE and AC = DF and Angle D = 90°

Proof -

In ∆ABC,

BC² = AB² + AC² - Given

In ∆ DEF

EF² = DE² + DF²

Therefore,

EF² = AB² + AC²

(Since AB = DE, AC = DF)

Therefore,

BC² = EF² ie - BC = EF

Now, In ∆ABC and ∆DEF

AB = DE - By Construction

AC = DF - By Construction

BC = EF

Therefore

∆ABC ≅ ∆DEF by SSS test.

Thus,

Angle A = Angle D - CPCT

But, Angle D = 90° ( As per construction)

Therefore

Angle A = 90°

Hence Proved! !!!!!!!!!!!!