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?

Question

Mathematics

Cheyenne Shah

7 November, 03:29

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?

+3

Answers (2)

Know the Answer?

Solomon Weeks · Answer 1

Step 2 isn't correct

Madden Oconnell · Answer 2

You're wrong only in the reasoning for step 2; everything else is correct.

1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD2. BC² = AC • DC 2̶.̶ ̶B̶C̶ ̶:̶ ̶D̶C̶ ̶=̶ ̶B̶C̶ ̶:̶ ̶A̶C̶ ̶b̶e̶c̶a̶u̶s̶e̶ ̶t̶r̶i̶a̶n̶g̶l̶e̶ ̶A̶B̶C̶ ̶i̶s̶ ̶s̶i̶m̶i̶l̶a̶r̶ ̶t̶o̶ ̶t̶r̶i̶a̶n̶g̶l̶e̶ ̶B̶D̶C̶

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 ADB and Angle BAC = Angle BAD4. AB² = AC • AD 4. AB : AD = AC : AB because triangle ABC is similar to triangle ADB5. AB² + BC² = AC • AD + AC • DC = AC (AD + DC) 5. Adding Statement 1 and Statement 26. AB² + BC² = AC²6. AD + DC = AC