Question

problem 1
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 ⅙, then each side length of p is multiplied by ⅙ 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 are multiplied by the scale factor, and angle measures remain the same.

Step2: Analyze option A

The scale factor can be a non - whole number, so side lengths of the scaled copy 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

Since angle measures are preserved in a scaled copy, and the angles of polygon $P$ are whole numbers ($40^{\circ},80^{\circ},125^{\circ},135^{\circ},250^{\circ}$), the angle measures of any scaled copy $Q$ are also whole numbers. So, option B is true.

Step4: Analyze option C

Polygon $P$ has exactly 1 right - angle, and since angle measures are preserved in a scaled copy, 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 $\frac{1}{6}$, then each side length of $P$ is multiplied by $\frac{1}{6}$ 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

Polygon $P$ has 2 acute angles ($40^{\circ}$ and $80^{\circ}$) and 3 obtuse angles ($125^{\circ},135^{\circ},250^{\circ}$). Since angle measures are preserved in a scaled copy, polygon $Q$ 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 $\frac{1}{6}$, then each side length of $P$ is multiplied by $\frac{1}{6}$ to get the corresponding side length of $Q$.
F. $Q$ has 2 acute angles and 3 obtuse angles.