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

When a polygon is scaled, side - lengths change according to the scale factor, and angle - measures remain the same.

Step2: Analyze option A

The side - lengths of a scaled copy are not necessarily whole numbers. They are multiplied by the scale factor, which can be a non - whole number. So, option A is false.

Step3: Analyze option B

Since angle measures are preserved in a scaled copy, and 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

Since angle measures are preserved in a scaled copy, and polygon P has exactly 1 right - angle, polygon 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 $\frac{1}{8}$, each side - length of P is multiplied by $\frac{1}{8}$ to get the corresponding side - length of Q. So, option D is true.

Step6: Analyze option E

Angle measures are not multiplied by the scale factor. They remain the same in a scaled copy. So, option E is false.

Step7: Analyze option F

Since angle measures are preserved in a scaled copy, and polygon P has 2 acute angles and 3 obtuse angles, polygon Q also 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 $\frac{1}{8}$, then each side length of P is multiplied by $\frac{1}{8}$ to get the corresponding side length of Q.
F. Q has 2 acute angles and 3 obtuse angles.