Question

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lesson 4 practice problems

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 $\frac{1}{3}$, then each side length of p is multiplied by $\frac{1}{3}$ 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.

1. here is quadrilateral abcd. quadrilateral pqrs is a scaled copy of quadrilateral abcd. point p corresponds to a, q to b, r to c, and s to d. if the distance from p to r is 3 units, what is the distance from q to s? explain your reasoning.

Explanation:

Step1: Recall properties of scaled - copies

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

Step2: Analyze each statement for polygon P and its scaled copy Q

A: Side - lengths of scaled copies are proportional, not necessarily whole numbers. False.
B: Angle - measures are equal in scaled copies, but no info about right angles always. False.
C: If scale factor is $\frac{1}{3}$, side - lengths of P are multiplied by $\frac{1}{3}$ to get Q's. True.
D: Angles are equal in scaled copies, not multiplied by scale factor. False.
E: Similar to D, angles are equal. False.
F: Angle - type distribution may change. False.

Answer:

C. If the scale factor between P and Q is $\frac{1}{3}$, then each side length of P is multiplied by $\frac{1}{3}$ to get the corresponding side length of Q.