Question

13. In triangle ABC , angle A+ angle B= angle C , then the triangle is(A) a right angle triangle (B) an isosceles triangle(C) an equilateral triangle (D) scalene​

Answer 1

• $\sf\fbox\pink{Appropriate Question}$

ABC is an isosceles triangle, right angled at C. Prove that AB 2 = 2AC 2 .

• $\sf\fbox\pink{Solution}$

In ∆ABC,

By Pythagorean Theorem,

(AB)² = (AC)² + (BC)²....(1)

Since, ∆ABC is an isosceles triangle,

∴ AC = BC ....(2)

∴ From (1) and (2),

(AB)² = 2(AC)²

$\green{ \underbrace{ \small \pink{ \underline{ \red{\sf \: Hence,\:Proved}}}}}$

Answer 2

\sf\fbox\pink{Appropriate Question}

Appropriate Question

ABC is an isosceles triangle, right angled at C. Prove that AB 2 = 2AC 2 .

\sf\fbox\pink{Solution}

Solution

In ∆ABC,

By Pythagorean Theorem,

(AB)² = (AC)² + (BC)²....(1)

Since, ∆ABC is an isosceles triangle,

∴ AC = BC ....(2)

∴ From (1) and (2),

(AB)² = 2(AC)²

\green{ \underbrace{ \small \pink{ \underline{ \red{\sf \: Hence,\:Proved}}}}}

Hence,Proved