Lesson 15: Practice Problems

Problem 1

Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope $\frac{1}{5} .$ Label each line with its slope.

A grid with a black, yellow and blue line. The yellow line crosses both the black and blue lines.

Problem 2

Draw three lines with slope 2, and three lines with slope $\frac{1}{3}$ . What do you notice?

Problem 3

The figure shows two right triangles, each with its longest side on the same line.

Triangle RST with side lengths: RS=4, ST=2. Triangle XYZ with side length YZ=3

Explain how you know the two triangles are similar.
How long is $X Y$ ?
For each triangle, calculate (vertical side) $\div$ (horizontal side).
What is the slope of the line? Explain how you know.

Problem 4 From Unit 2 Lesson 14

Triangle $A$ has side lengths 3, 4, and 5. Triangle $B$ has side lengths 6, 7, and 8.

Explain how you know that Triangle $B$ is not similar to Triangle $A$ .
Give possible side lengths for Triangle $B$ so that it is similar to Triangle $A$ .

Problem 5

A runner ran $\frac{2}{3}$ of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.

How long did it take to run the entire race?
How many minutes did it take to run 1 kilometer?

Problem 6 From Unit 2 Lesson 8

Triangle $A B C$ is a scaled copy of triangle $D E F$ . Side $A B$ measures 12 cm and is the longest side of $A B C$ . Side $D E$ measures 8 cm and is the longest side of $D E F$ .

Triangle $A B C$ is a scaled copy of triangle $D E F$ with what scale factor?
Triangle $D E F$ is a scaled copy of triangle $A B C$ with what scale factor?