Question

The figure below shows two triangles EFG and KLM.
Which step can be used to prove that triangle EFG is also a right triangle?
Answer

Prove that a + b is greater than c in triangle EFG so c2 = a2 + b2.

Prove that KL = EF so in triangle KLM c2 = a2 + b2 which makes triangle EFG a right triangle.

Prove that the sum of the squares of a and c in triangle EFG is greater than square of b in triangle KLM.

Prove that the sum of the squares of a and b in triangle KLM is greater than square of c in triangle EFG.

Answer 1

Answer

Prove that KL = EF so in triangle KLM c2 = a2 + b2 which makes triangle EFG a right triangle.

Explanation
For a right triangle, the sum of the legs squared is equal to the hypotenuse squared. 
So, in the triangle EFG, a²+b²=c².
To make EFG a right triangle at G, we can compared ΔEFG and ΔKLM. Line EF=KL.
The correct answer from the choices is; "Prove that KL = EF so in triangle KLM c2 = a2 + b2 which makes triangle EFG a right triangle".

Answer 2

Answer:

Option 2nd is correct.

Step-by-step explanation:

In right angle triangle:

Pythagoras theorem follows which is:

Here, c= hypotenuse b is one side and a is the other side.

Therefore, according to Pythagoras theorem Option 1,3 and 4 are discarded.

Option 2nd is correct because KL=EF and triangle KLM and EFG follows Pythagoras theorem which makes them a right angle triangle.