Question

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

Explanation:

Step1: Recall the proportion rule for similar triangles

For similar triangles, the ratios of corresponding sides are equal. If two triangles are similar, say \(\triangle ABC\) and \(\triangle DEF\), then \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\) (by the Side - Side - Side similarity criterion for similar triangles).

Step2: Analyze each option

• Option a: \(\frac{AB}{DE}=\frac{AC}{DF}\) is in line with the proportion rule of corresponding sides of similar triangles.
• Option b: \(AB = AC=DE = DF\) is about equality of side lengths, not a proportion for similar triangles (this would be for congruent triangles in some cases, not the general proportion for similar triangles).
• Option c: \(AB + DE=AC + DF\) is an addition relationship, not a proportion relationship relevant to similar triangles.
• Option d: \(AB\times DE=AC\times DF\) is a product relationship, not the ratio - based proportion relationship for similar triangles.

Answer:

A. \(AB/DE = AC/DF\)