Question

In ∆ ABC, AC2=AB2+BC2 and ∆ LMN is constructed such that ∟M=90°, LM=AB

and MN=BC, Prove that:

∟B=90° (write only the proof with reasons.)​

Answer 1

Step-by-step explanation:

Given :- AC²=AB²+ BC²

∠M=90°

LM=AB

To- prove :- ∠B = 90°

Proof:-

In △ABC,

⇒ (AC)² =(BC)² +(AB)² [ Given ] --- ( 1 )

Pythagoras theorem,

⇒ (Hypotenuse)² =(oneside)² +(otherside)²---- ( 2 )

Comparing ( 1 ) and ( 2 ) we get, AC is a hypotenuse of a triangle.

⇒ Hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

⇒ Opposite angle of AC is ∠B.

∴ ∠B is a right angle of △ABC.

hence proved,

∠B=90°