Question

1. consider the given right triangular prism and the cross section formed by a plane intersecting the prism parallel to its bases.

a. the base of the right triangular prism is drawn. sketch the cross section and label the side lengths with the appropriate measurements.
b. is the cross section a scale drawing of the base? if so, determine the scale factor. if not, explain why not.

Explanation:

Step1: Analyze cross section properties

A plane parallel to the bases of a right prism creates a cross section congruent to the base. So the cross section is a triangle with side lengths 11 in, 11 in, 9 in.

Step2: Define scale drawing condition

A scale drawing has all side lengths scaled by the same positive factor. Congruent figures have a scale factor of 1, which fits this definition.

Step3: Calculate scale factor

Scale factor = $\frac{\text{Cross section side length}}{\text{Base side length}} = \frac{11}{11} = 1$, or $\frac{9}{9} = 1$.

Answer:

a. The cross section is an isosceles triangle with side lengths labeled: two sides of 11 inches and one side of 9 inches (congruent to the given base triangle).
b. Yes, the cross section is a scale drawing of the base. The scale factor is 1, since the cross section is congruent to the base (all corresponding side lengths are equal).