Question

AB is congruent to DE because segment DE was constructed so that DE = AB. BC is congruent to EF because segment EF was constructed so that EF = BC. Since ADEF is a right triangle, DE+ EF? = DF? by the We are given that AB + BC2 = AC? Since DE = AB and EF = BC, DE2 + EF2 = AC? by the Also, DF2 = AC2 by the Taking the square root of both sides of the equation gives DF = AC. So, AC is congruent to DF by the definition of congruence. Applying the AABC - ADEF. By CPCTC, ZB _ZE. Therefore ZB is a right angle and AABC is a right triangle.

Answer 1

The question involves proving that a triangle is a right triangle by using congruent segments and the Pythagorean theorem, leading to the conclusion that ABC is indeed a right triangle.

Step-by-step explanation:

The problem revolves around proving that a certain ABC triangle is a right triangle, using properties of congruent segments and the Pythagorean theorem. Given that segments AB and DE are congruent, as well as segments BC and EF, and knowing that ADEF is a right triangle, we can use the theorem to deduce that DE2 + EF2 = DF2, which implies that AC is congruent to DF. Hence, because corresponding parts of congruent triangles are congruent (CPCTC), angle B in triangle ABC is a right angle, making ABC a right triangle as well.

Answer 2

pythagorean theorem, division, substatution, SAS

Step-by-step explanation:

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