Mathematics, 10.06.2024 16:40 amazinga

# Given: △ABC with a2 + b2 = c2 and right △DEF constructed with legs a and b and hypotenuse n

Prove: △ABC is a right triangle.

Complete the missing parts of the paragraph proof.

Proof:

We are given a2 + b2 = c2 for △ABC and right

△DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the

. By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get

c = n. By

, triangles ABC and DEF are congruent. Since it is given that

∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by

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Given: △ABC with a2 + b2 = c2 and right △DEF constructed with legs a and b and hypotenuse n

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