Question

Given △GHI and △JKL, GI = 5, HI = 4, JK = 4, and JL = 5, what else do you need to know to prove the two triangles are congruent using HL? You need to know that angles and are right angles because HL only works with right triangles.

Answer 1

Answer:

△ GHI ≅ △ JKL. (Proved)

Step-by-step explanation:

In triangle Δ GHI, GI = 5 and HI = 4.

If we consider the triangle is a right triangle having hypotenuse = 5 and any other leg = 4.

Then this will follow the Pythagoras theorem as 3² + 4² = 5², where 3 is the other leg.

Therefore, Δ GHI is a right triangle having hypotenuse 5 and one leg 4.

Similarly, we can prove that △ JKL is also a right triangle(Since JK = 4 and  JL = 5), having hypotenuse 5 and one leg 4.

Therefore, applying HL rule, we cam conclude △ GHI ≅ △ JKL. (Proved)