Question

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


Which justification is incorrect? (1 point)

Justification 3
Justification 4
Justification 2
Justification 1

Also to clarify, I chose 4 on my test. It’s actually 2. I just need someone to explain why it’s justification 2.

Answer 1

Answer:

Solution:

Given : In triangle ABC right angled at B.

To Prove :

Construction: Draw B D perpendicular AC.

Proof: 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD  

2. = 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.   = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD  

5.

= AC (AD + DC)  

6. Adding Statement 1 and Statement 2  

7.

→→→Statement 3 is incorrect.It should be replaced by, Angle ABC = Angle ADB and Angle B AC = Angle BAD .

hope i could help also if u have time please mark me as brainlest