"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)
6. Adding Statement 1 and Statement 2
7. AB2 + BC2 = AC2
Which of the first four steps is the error?"

Question

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Respuesta :

ErinTomei ErinTomei · Answer 1 · 2017-01-13T19:32:30+01:00

Step two is incorrect

Answer Link

Аноним Аноним · Answer 2 · 2019-01-15T09:19:23+01:00

Solution:

Given : In triangle ABC right angled at B.

To Prove : [tex]AB^2 + BC^2= AC^2[/tex]

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.[tex]BC^2[/tex] = 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. [tex]AB^2[/tex] = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD

5.[tex]AB^2 + BC^2 = AC \times AD + AC \times DC[/tex]

= AC (AD + DC)

6. Adding Statement 1 and Statement 2

7. [tex]AB^2 + BC^2= AC^2[/tex]

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