Question

problem 3
polygon b is a scaled copy of polygon a.
a. what is the scale factor from polygon a to polygon b? explain your reasoni
b. find the missing length of each side marked with ? in polygon b.
c. determine the measure of each angle marked with ? in polygon a.
problem 4
complete each equation with a number that makes it true.
a. 8• ____ = 40
b. 8+ ____ = 40
c. 21÷ ____ = 7
d. 21− ____ = 7
e. 21• ____ = 7

Explanation:

Problem 3

a. Scale Factor from A to B

Step1: Identify Corresponding Sides

In Polygon A, a side is 2.5, and in Polygon B, the corresponding side is 5.

Step2: Calculate Scale Factor

Scale factor = $\frac{\text{Length in B}}{\text{Length in A}}$ = $\frac{5}{2.5}$ = 2.

Step1: For the side with length 1.5 in A

Multiply by scale factor 2: $1.5 \times 2 = 3$.

Step2: For the side with length 2.5 (other) in A

Multiply by 2: $2.5 \times 2 = 5$.

Step3: For the side with length 7 in A

Multiply by 2: $7 \times 2 = 14$.

Scaled copies have equal angles (similar polygons). So the angle marked 82° in B is also 82° in A. For the other angle, sum of angles in a quadrilateral is 360°, but since it's a scaled copy, corresponding angles are equal. Wait, the 53° in B corresponds to the same in A? Wait, no—wait, Polygon A and B are similar, so corresponding angles are equal. So the angle marked? in A (corresponding to 82° in B) is 82°, and the other? (corresponding to 53° in B) is 53°? Wait, no, let's check: in similar polygons, angles are congruent. So the angle with 82° in B is equal to the corresponding angle in A, and the 53° in B is equal to its corresponding angle in A. So the missing angles in A are 82° and 53° (matching the marked angles in B, as they are corresponding angles in similar polygons).

Answer:

2 (since 5 ÷ 2.5 = 2, so the scale factor is 2)

b. Missing Lengths in B