Question

1. Given: BJ≅ CF

Which additional statement could you use to prove that ∆BJK ≅ ∆CFH by the HL Theorem?

A) JK≅ FH

B) ∠B ≅ ∠C

C) ∠BJK ≅ ∠CFH

D) AJ≅ A F

Answer 1

The answer is A. JK is congruent to FH

Answer 2

RHL theorem States that if, in a right angled triangle , Hypotenuse and one side of a triangle is equal to hypotenuse and other side , then the two Right triangles are congruent.

Assuming that ∆B J K, ∆ CF H are two right triangles, considered for Congruency.

If, BJ≅ CF → [Given]

then, we must find other side ,which are congruent.

So, J K ≅ F H

If , B J and C F are hypotenuse , then JK and F H are two other sides of right triangle, and if K J and H F are hypotenuse , then JB and F C are two other sides.

Option A: JK≅ FH