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.
a
b
c
b
Triangle DEF is a right triangle
a² +6² c²
Click the arrows to choose an answer from each menu.
To prove triangle JKL is a right triangle, we must show that Choose... is a right angle.
Since triangle DEF is given to be right triangle, the Pythagorean theorem can be applied to
determine that Choose...
We already know that a² + b2 = c in triangle JKL, SO
these two equations show that Choose...
which is enough to
prove that triangles DEF and JKL are congruent triangles. Then, triangle JKL must be a
right triangle because Choose...
hi

Answer 1

Triangle JKL is proved to be a right triangle by demonstrating that it has side lengths that satisfy the Pythagorean theorem a² + b² = c². Because triangle DEF is a given right triangle with the same side lengths that satisfy the theorem, triangle JKL must also be a right triangle.

Step-by-step explanation:

To prove that triangle JKL is a right triangle, we must demonstrate that one of its angles is a right angle. Since triangle DEF is given to be a right triangle, we apply the Pythagorean theorem, which establishes that if a triangle has sides of length a, b, and c, with c being the hypotenuse, the relationship a² + b² = c² is satisfied.

We already know that a² + b² = c² for triangle JKL. These two equations confirm that triangle DEF and triangle JKL have side lengths that satisfy the Pythagorean theorem. Because we know triangle DEF is a right triangle and triangle JKL satisfies this necessary condition of right triangles, it follows that triangle JKL must also be a right triangle by the Converse of the Pythagorean theorem.

Therefore, since both triangles satisfy a² + b² = c² and triangle DEF is a right triangle by definition, we can conclude that triangle JKL is also a right triangle. This is because it satisfies the necessary condition for a triangle to be classified as a right triangle, and therefore triangles DEF and JKL are congruent in terms of side lengths and right angles, making triangle JKL a right triangle.

Answer 2

Angle L,

a^2+b^2=DE^2

De^2=c^2 and CE=c

angle L=F