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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 BCD 2. BC2 = AC × DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC 3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD 4. AB2 = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD 5. AB2 + BC2 = AC × AD + AC × DC = AC (AD + DC) 5. Adding Statement 1 and Statement 2 6. AB2 + BC2 = AC2

Mathematics
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