Question

prove that △abc is a right triangle. select the correct answer from each drop - down menu.
$overline{ab}$ is congruent to $overline{de}$ because segment de was constructed so that $de = ab$. $overline{bc}$ is congruent to $overline{ef}$ because segment ef was constructed so that $ef = bc$. since △def is a right triangle, $de^{2}+ef^{2}=df^{2}$ by the we are given that $ab^{2}+bc^{2}=ac^{2}$. since $de = ab$ and $ef = bc$, $df^{2}=ac^{2}$ by the also, taking the square root of both sides of the equation gives $df = ac$. by the definition of congruence. applying the, △abc ≅ △def. by cpctc, ∠b ≅ ∠e. therefore ∠b is a right angle and △abc is a right triangle.
question 2
suppose triangles p, q, and r have sides with the given measurements.

• triangle p: 12, 24, and 30
• triangle q: 9, 40, and 41
• triangle r: 5, 18, and 21

which triangle is a right triangle? explain your reasoning.

Explanation:

Answer:

1. Pythagorean theorem; transitive property of equality; SSS congruence theorem
2. Triangle Q is a right triangle because $9^2 + 40^2 = 81 + 1600 = 1681 = 41^2$, satisfying the Pythagorean theorem.