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 = 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?"

Answer 1

Answer: There is no error in the first four steps. These steps are correctly stating and applying the properties of similar triangles. Specifically, if two triangles are similar, then their corresponding sides are proportional. This means that if we let AC/AB = x and AD/BC = x, then we can write AC/AB = AD/BC. From this, we can obtain the proportionality relationship AC/BC = AD/AB. This proportionality relationship can then be squared to obtain AC^2/BC^2 = AD^2/AB^2, which is equivalent to BC^2/AC^2 = AB^2/AD^2.

Step-by-step explanation: