Question

course activity: pythagorean triples
since de = ab and ef = bc, de² + ef² = ac² by the substitution property of equalit
df² = ac² by the pythagorean theorem. taking the square root of both sid
equation gives df = ac. so, \\(\overline{ac}\\) is congruent to \\(\overline{df}\\) by the definition of congruence. applyin
sss criterion, \\(\triangle abc \cong \triangle def\\). by cpctc, \\(\angle b \cong \angle e\\). therefore \\(\angle b\\) is a right angle and
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:

Triangle Q is a right triangle because its side lengths satisfy the Pythagorean theorem: $9^2 + 40^2 = 81 + 1600 = 1681 = 41^2$.