Question

select all the statements that must be true for any scaled copy q of polygon p.
a the side lengths are all whole numbers.
b the angle measures are all whole numbers.
c q has exactly 1 right angle.
d if the scale factor between p and q is ⅕, then each side length of p is multiplied by ⅕ to get the corresponding side length of q.
e if the scale factor is 2, each angle in p is multiplied by 2 to get the corresponding angle in q.
f q has 2 acute angles and 3 obtuse angles.

Explanation:

Step1: Recall properties of scaled - copies

Scaled copies of polygons have proportional side - lengths and equal angle - measures.

Step2: Analyze option A

The side - lengths of a scaled copy are proportional to the original. They are not necessarily whole numbers. For example, if the scale factor is $\frac{1}{3}$, side - lengths of the original polygon multiplied by $\frac{1}{3}$ may not be whole numbers. So, option A is false.

Step3: Analyze option B

The angle measures of a scaled copy are the same as the original polygon. Since the angles in polygon P are whole numbers, the angle measures in Q are also whole numbers. So, option B is true.

Step4: Analyze option C

Polygon P has exactly 1 right - angle. Scaled copies have the same shape, so Q also has exactly 1 right - angle. So, option C is true.

Step5: Analyze option D

By the definition of a scale factor, if the scale factor between P and Q is $\frac{1}{5}$, then each side - length of P is multiplied by $\frac{1}{5}$ to get the corresponding side - length of Q. So, option D is true.

Step6: Analyze option E

The angle measures of similar polygons (scaled copies) are equal. We do not multiply angle measures by the scale factor. So, option E is false.

Step7: Analyze option F

The number of acute and obtuse angles in a scaled copy is the same as in the original polygon. Polygon P has 2 acute angles and 3 obtuse angles, so Q has 2 acute angles and 3 obtuse angles. So, option F is true.

Answer:

B. The angle measures are all whole numbers.
C. Q has exactly 1 right angle.
D. If the scale factor between P and Q is $\frac{1}{5}$, then each side length of P is multiplied by $\frac{1}{5}$ to get the corresponding side length of Q.
F. Q has 2 acute angles and 3 obtuse angles.