Question

In an isosceles triangle ABC If AC=BC and AB Square equals to 2AC square. Then measure of angle C is?

Answer 1

Answer:

Step-by-step explanation:

Given-AC=BC and (AB)^2=(2AC)^2

TO PROVE-Measure of anle C

PROOF-as given,

(AB)^2=(2AC)^2

(AB)^2=(AC+AC)^2

(AB)^2=(AC)^2+(BC)^2 (as givenAC=BC)

So,by converse of pythagoras theorem

Angle C =90°

Answer 2

Correct question:-

ABC is an isosceles triangle with AC=BC. If AB^2=2AC^2 prove that ABC is a right triangle.

Given that:-

ABC is an isosceles triangle .

AC = BC

AB^2 = 2AC^2

To prove:-

ABC is a right triangle

_____________________________

Proof

AB² = 2AC² - (Given)

AB² = AC² + AC²

AB² = AC² + BC² - (As AC = BC)

Thus, AB is the largest side i.e the (Hypotenuse).

By the Converse of Pythagoras theorem,

∠C = 90°

Hence its a right angle triangle.