Question

1. which of the following is an example of a correct proportion for similar triangles? a. ab/de = ac/df b. ab - ac = de - df c. ab + de = ac + df d. ab × de = ac × df 2. which of the following is not a step in proving triangle similarity using aa? a. identify two pairs of corresponding angles b. conclude the triangles are similar c. prove that the triangles are congruent d. show that these angles are congruent 3. which of the following is a correct similarity statement for triangles △jkl and △mno if they are similar by aa similarity? a. △jkl > △mno b. △jkl - △mno c. △jkl = △mno d. △jkl ~ △mno

Explanation:

Step1: Recall similar - triangles property

For similar triangles, the ratios of corresponding sides are equal. If \(\triangle ABC\sim\triangle DEF\), then \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\). So for question 1, option a is correct.

Step2: Recall AA - similarity proof steps

In the AA (angle - angle) similarity criterion, we identify two pairs of corresponding congruent angles and then conclude that the triangles are similar. Proving congruence of triangles is not a part of proving similarity using AA. So for question 2, option c is correct.

Step3: Recall similarity notation

The symbol for similarity of two triangles is \(\sim\). So if \(\triangle JKL\) and \(\triangle MNO\) are similar, the correct similarity statement is \(\triangle JKL\sim\triangle MNO\). For question 3, option d is correct.

Answer:

1. A. \(AB/DE = AC/DF\)
2. C. Prove that the triangles are congruent
3. D. \(\triangle JKL\sim\triangle MNO\)