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Gabylovesyou
 11 months ago
Best ResponseYou've already chosen the best response.1Look at the right triangle ABC. Right triangle ABC has a right angle at B. Segment BD meets segment AC at a right angle. A student made the following chart to prove that AB2 + BC2 = AC2. Statement Justification 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle DCB 2. BC2 = AC x DC 2. BC ÷ DC = BC ÷ AC because triangle ABC is similar to triangle BDC 3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle ADB and Angle BAC = Angle DAB 4. AB2 = AC x AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB 5. AB2 + BC2 = AC x AD + AC x D = AC (AD + DC) 5. Adding Statement 1 and Statement 2 6. AB2 + BC2 = AC2 6. AD + DC = AC What is the flaw in the student's proof? Justification 3 should be "Angle ABC = Angle BAD and Angle BAC = Angle ABD." Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD." Justification 2 should be "BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC." Justification 1 should be "Angle ABC = Angle BCD and Angle BCA = Angle DBC.
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