Question

In the diagram below, BC = QR = x, AC = PR = y, and triangle PQR is a right
triangle. Use the drop-down menus to complete the proof that if the equation
22 + y2 = z2 is true of the side lengths in triangle ABC, then triangle ABC must be a right
triangle.
P
y у
y
B
R
х
Q
x2 + y2 = 22
Triangle PQR is a right triangle
Click the arrows to cho
from each menu.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to

Answer 1

Applying the Pythagorean theorem, we have ΔPQR ≅ ΔABC. then we would have: ∠ACB = ∠PRQ = 90°

What is the Pythagroean Theorem?

The pythagorean theorem states that the square of the longest side (hypotenuse) of a right triangle is always equal to the sum of the squares of the other two sides (legs) of the right triangle.

Since we know that ΔPQR is a right triangle, then:

x² + y² = PQ²

We are also given that x² + y² = z², so by substitution, we have:

z² = PQ², which makes both triangles have corresponding congruent sides. Therefore, ΔPQR ≅ ΔABC.

Using the corresponding parts of the congruent triangles, we can conclude that: ∠ACB = ∠PRQ = 90°.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/343682

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