Question

A student made the following chart to prove that AB2 + BC2 = AC2. (SEE ATTACHMENT)

Which of the first four steps is the error?

Answer 1

A step that contains an error is justification 4.

Statement Justification

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

The Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two triangles that are formed would be similar to each other, as well as the original triangle.

By applying the Right Triangles Similarity Theorem, we can reasonably and logically deduce that both triangle ABC and triangle BDA are similar triangles.

Since triangle ABC is similar to triangle BDA, we have the following proportions;

AB/AD = AC/AB

`AB^2` = AC × AD

Answer 2

"Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD" is the one step among the following choices given in the question that has the error. The correct option among all the options that are given in the question is the third option or option "3". I hope the answer has helped you.