Question

In the diagram below, DF = JL = a, FE = LK = b, and triangle DEF is a right triangle.
Use the drop-down menus to complete the proof that if the equation a² + b2 = c2 is true of
the side lengths in triangle JKL, then triangle JKL must be a right triangle.

Answer 1

ΔDEF and ΔJKL are congruent to each other.

.

What is Congruency?

Congruent triangles are triangles that have the same size and shape

This means that the corresponding sides are equal and the corresponding angles are equal.

Given

DF = JL = a, FE = LK = b, ΔDEF is a right triangle.

As Pythagoras theorem can be used in ΔDEF.

Also  ΔJKL Hence angle K is the right-angle.

As, ∠F = ∠L = 90°,

         DF = JL = a,

       FE = LK = b

Hence, ΔDEF and ΔJKL are congruent to each other.

Learn more about this concept here:

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