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

attachment

anonymous · Answer

Which of the first four steps is the error

anonymous · Answer

I've already elimianted the first choice

anonymous · Answer

I think it is the 3rd one. what do you all think?

anonymous · Answer

@Qwerty90 , what makes you think that the 3rd option is wrong ??

anonymous · Answer

I'll tell you are right/wrong after you tell me your reason

anonymous · Answer

The angles  don't correspond because they don't have the same angle?

anonymous · Answer

Good job @Qwerty90

anonymous · Answer

Thanks!

anonymous · Answer

yw :)