Lesson 3: Practice Problems

Problem 1

Here is Quadrilateral $A B C D$ .

Quadrilateral ABCD is on a grid. Point a is 2 units right and 4 units down from the edge of the grid. Point B is 2 units right and 2 units up from point A. Point C is 6 units right from point A. Point D is 2 units right and 4 units down from point A.

Quadrilateral $P Q R S$ is a scaled copy of Quadrilateral $A B C D$ . 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.

Problem 2

Rectangles $P$ , $Q$ , $R$ , and $S$ are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.

Four rectangles, labeled P, Q, R and S. Each rectangle is a scaled copy of one another. Ranked in order from least to greatest, the area of the rectangles are as follows: the area of P is equal to S, which are less than the area of Q, which is less than the area of R.

from $P$ to $Q$
from $P$ to $R$
from $Q$ to $S$
from $Q$ to $R$
from $S$ to $P$
from $R$ to $P$
from $P$ to $S$

Problem 3

Triangle $S$ and Triangle $L$ are scaled copies of one another.

Two triangles labeled S and L on a grid. Triangle S has a horizontal base of 2 units and a height of 4 units. Triangle L has a horizontal base of 4 units and a height of 8 units.

What is the scale factor from $S$ to $L$ ?
What is the scale factor from $L$ to $S$ ?
Triangle $M$ is also a scaled copy of $S$ . The scale factor from $S$ to $M$ is $\frac{3}{2}$ . What is the scale factor from $M$ to $S$ ?

Problem 4

Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.

Problem 5

Quadrilateral $A$ has side lengths 2, 3, 5, and 6. Quadrilateral $B$ has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other? Explain.

Problem 6 From Unit 1 Lesson 13

The line has been partitioned into three angles.

A line partitioned into 3 angles. From left to right: 39, 99, and 42 degrees.

Is there a triangle with these three angle measures? Explain.