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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Look 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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