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.
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 = 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 DAB
4. AB2 = AC x AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB
5. AB2 + BC2 = AC x AD + AC x D = AC (AD + DC) 5. Adding Statement 1 and Statement 2
6. AB2 + BC2 = AC2 6. AD + DC = AC
What is the flaw in the student's proof?
Justification 3 should be "Angle ABC = Angle BAD and Angle BAC = Angle ABD."
Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD."
Justification 2 should be "BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC."
Justification 1 should be "Angle ABC = Angle BCD and Angle BCA = Angle DBC.