Question

Which of the following can be used to prove that triangle EFG is also a right triangle?

Prove that the sum of a and c is greater than b.
Prove that the sum of a and b is greater than c.
Prove that the ratio of EF and KL is greater than 1 and hence, the triangles are similar by AA postulate.
Prove that KL is equal to c by Pythagorean Theorem.

Answer 1

Which of the following can be used to prove that triangle EFG is also a right triangle?

Prove that the sum of a and c is greater than b.
Prove that the sum of a and b is greater than c.
Prove that the ratio of EF and KL is greater than 1 and hence, the triangles are similar by AA postulate.
Prove that KL is equal to c by Pythagorean Theorem.

The correct answer is:
Prove that KL is equal to c by Pythagorean Theorem.

It can also be "Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML"

Answer 2

Prove that KL is equal to c by Pythagorean Theorem.

Explanation:

In the two triangles triangle KLM is a right triangle with sides a and b as the two legs of the right triangle .We can apply Pythagorean Theorem to find KL.

In triangle KGF two sides are a and b .If we prove KL=EF then Pythagorean Theorem will be true for triangle KGF and hence we can prove triangle KGF to be a right triangle.

The correct option to prove triangle KGF to be a right triangle is to Prove that KL is equal to c by Pythagorean Theorem.