Question

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:

Answer 1

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 ADB
5. AB2 + BC2 = AC • AD + AC • DC = AC (AD + DC) 5. Adding Statement 1 and Statement 2
6. AB2 + BC2 = AC2 6. AD + DC = AC

Which justification is incorrect?
Justification 4
Justification 1
Justification 2
Justification 3

Answer 2

@jim_thompson5910

Answer 3

@ganeshie8

Answer 4

Please help!