Question

camden is creating a model of a pyramid. the model created will need to be scaled up from the blueprint. if segments de and ab are parallel, which of the following expressions will help camden determine the length of dc? (1 point)

Explanation:

Step1: Identify Similar Triangles

Since \( DE \parallel AB \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle CDE \sim \triangle CAB \) (similar triangles) because corresponding angles are equal (alternate interior angles and common angle at \( C \)).

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{DC}{AC}=\frac{DE}{AB} \) (or other corresponding sides ratio). To find \( DC \), we can rearrange this proportion. If we know \( AC \), \( DE \), and \( AB \), we can solve \( DC = AC\times\frac{DE}{AB} \).

(Note: Since the problem is about similar triangles and proportionality, the key is recognizing the similar triangles and setting up the ratio of corresponding sides.)

Answer:

The expression involves the ratio of corresponding sides of similar triangles \( \triangle CDE \) and \( \triangle CAB \), e.g., \( DC = AC\times\frac{DE}{AB} \) (or equivalent proportion based on known side lengths).