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

Answer 1

What is the flaw in the student's proof?
Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD."

Justification 1 should be "Angle ABC = Angle BCD and Angle BCA = Angle DBC."

Justification 2 should be "BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC."

Justification 3 should be "Angle ABC = Angle ADB and Angle BAC = Angle DAB."

Answer 2

@dcknox123 @ikram002p @mathstudent55

Answer 3

i would say the third one