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:

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



What is the first incorrect justification?

Answer 1

Justification 2

Explanation:

I took the test and it was correct

Answer 2

The first incorrect justification is in step 2.

Explanation:

Step 2. BC2 = AC • DC

2. BC ÷ DC = BC ÷ AC because triangle ABC is similar to triangle BDC

It's supposed to be AC ÷ BC not BC ÷ AC.