Question

consider the enlargement of the triangle.
which statement is true about setting up a proportion
to solve for the missing measure?

o corresponding parts must be in different positions.
o corresponding parts must be in the same position.
o the two ratios are not equal.
o the enlargement is not proportional to the original
figure.

Explanation:

Step1: Understand the concept of proportion for similar figures

When dealing with an enlargement (similar figures), the ratios of corresponding sides are equal. Corresponding parts must be in the same position. For example, if one side in the original triangle is \(6\) mm and the corresponding side in the enlarged triangle is \(16\) mm, and another side in the original is \(9\) mm with its corresponding side \(x\) in the enlarged triangle.

Step2: Analyze each option

• Option 1: The enlargement is proportional. Since they are similar (enlargement), ratios of corresponding sides are equal. So this option is wrong.
• Option 2: The two ratios (of corresponding sides) are equal. For similar figures (enlargement), \(\frac{6}{16}=\frac{9}{x}\) (ratios of corresponding sides). So this option is wrong.
• Option 3: Corresponding parts must be in the same position. For similar triangles (enlargement), when setting up a proportion like \(\frac{\text{original side}_1}{\text{enlarged side}_1}=\frac{\text{original side}_2}{\text{enlarged side}_2}\), the sides must correspond in position. This is correct.
• Option 4: Corresponding parts must be in the same position (not different positions) for the proportion to hold. So this option is wrong.

Answer:

Corresponding parts must be in the same position.