Question

prove that $\triangle abc$ 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 $\triangle def$ is a right triangle, $de^{2}+ef^{2}=df^{2}$ by the pythagorean theorem. we are given that $ab^{2}+bc^{2}=ac^{2}$. since $de = ab$ and $ef = bc$, $de^{2}+ef^{2}=ac^{2}$ by the. also, $df^{2}=ac^{2}$ by the. the equation gives $df = ac$. so, $\overline{ac}$ is congruent to $\overline{df}$ by the, $\triangle abc\cong\triangle def$. by cpctc, $\angle b\cong\angle e$. so $\triangle abc$ 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. substitution property of equality; transitive property of equality; square root property of equality; SSS triangle congruence theorem
2. triangle Q; $9^2 + 40^2 = 81 + 1600 = 1681 = 41^2$