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:
First one is the Statement and the second one is the 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 = BC ÷ AC because triangle ABC is similar to triangle BDC
3. Triangle ABC is similar to triangle ABD
3. Angle ABC = Angle ADB and Angle BAC = Angle BAD
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
