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

Question

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

anonymous · Answer

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