Lesson 10: Practice Problems

Problem 1

A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many unique triangles can be drawn that fit that description? Explain or show your reasoning.

Problem 2

A triangle has one side that is 5 units long and an adjacent angle that measures $25^{\circ}$ . The two other angles in the triangle measure $90^{\circ}$ and $65^{\circ}$ . Complete the two diagrams to create two different triangles with these measurements.

Two diagrams-A triangle with one side 5 units long and an adjacent angle that measures 25 degrees with differing adjacent side lengths.

Problem 3

Is it possible to make a triangle that has angles measuring 90 degrees, 30 degrees, and 100 degrees? If so, draw an example. If not, explain your reasoning.

Problem 4 From Unit 7 Lesson 2

Segments $C D$ , $A B$ , and $F G$ intersect at point $E$ . Angle $F E C$ is a right angle. Identify any pairs of angles that are complementary.

Three lines intersecting at point E. Lines are labeled AB, CD, FG.

Problem 5 From Unit 5 Lesson 15

Match each equation to a step that will help solve the equation for $x$ .

$3 x = - 4$
$- 4.5 = x - 3$
$3 = \frac{- x}{3}$
$\frac{1}{3} = - 3 x$
$x - \frac{1}{3} = 0.4$
$3 + x = 8$
$\frac{x}{3} = 15$
$7 = \frac{1}{3} + x$

Add $\frac{1}{3}$ to each side.
Add $\frac{- 1}{3}$ to each side.
Add $3$ to each side.
Add $- 3$ to each side.
Multiply each side by 3.
Multiply each side by $- 3$ .
Multiply each side by $\frac{1}{3}$ .
Multiply each side by $\frac{- 1}{3}$ .

Problem 6 From Unit 4 Lesson 8

If you deposit $300 in an account with a 6% interest rate, how much will be in your account after 1 year?
If you leave this money in the account, how much will be in your account after 2 years?