Answered

"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 = 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. AB2 = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD
  5. AB2 + BC2 = AC × AD + AC × DC

= AC (AD + DC)

  1. Adding Statement 1 and Statement 2
  2. AB2 + BC2 = AC2

Which of the first four steps is the error?"

Verified Answer :

ErinTomei

Step two is incorrect

Solution:

Given : In triangle ABC right angled at B.

To Prove : \(AB^2 + BC^2= AC^2\)

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.\(BC^2\) = 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. \(AB^2\)  = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD  

5.\(AB^2 + BC^2 = AC \times AD + AC \times DC\)

= AC (AD + DC)  

6. Adding Statement 1 and Statement 2  

7. \(AB^2 + BC^2= AC^2\)

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

View image Anonymous

Related Questions