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

Explanation:

Step1: Recall the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal.

Step2: Analyze each option

• Option a: \(AB\times DE = AC\times DF\) is not the correct form of side - ratio equality for similar triangles.
• Option b: \(AB = AC=DE = DF\) is not a proportion, it is an equality of lengths.
• Option c: \(AB + DE=AC + DF\) is an addition relation, not a proportion for similar triangles.
• Option d: \(\frac{AB}{DE}=\frac{AC}{DF}\) is in the form of \(\frac{\text{side of first triangle}}{\text{corresponding side of second triangle}}=\frac{\text{another side of first triangle}}{\text{corresponding side of second triangle}}\), which is the correct proportion for similar triangles.

Answer:

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