Lesson 5 Measured Reasoning Practice Understanding

Ready

Find the missing side in each right triangle. Triangles are not drawn to scale.

1.

2.

3.

4.

5.

6.

7.

Based on ratios between side lengths, which of the previous right triangles are mathematically similar to each other? Name the triangles and write the proportion that demonstrates that they are similar.

Set

8.

Line $m ∥ n$ and $o ∥ p$ , find the values of angles $x$ , $y$ , and $z$ . Also, find the lengths of $a$ , $b$ , and $c$ .

9.

Line $q ∥ r ∥ s$ and $t ∥ u$ and $p ∥ w ∥ v$ , find the values of angles $x$ , $y$ , and $z$ . Also, find the lengths of $a$ , $b$ , $c$ , $d$ , $e$ , and $f$ .

Go

Solve each equation.

10.

$3 x - 5 = 2 x + 7$

11.

$\frac{5}{7} = \frac{x}{21}$

12.

$\frac{3}{x} = \frac{18}{5 x + 2}$

13.

$\frac{1}{2} x - 7 = \frac{3}{4} x - 8$

14.

$17 + 3 (x - 5) = 2 (x + 3)$

15.

$\frac{x + 5}{6} = \frac{3 (x + 2)}{9}$

16.

$x + 2 + 3 x - 8 = 90$

17.

$\frac{5}{12} = \frac{x}{8}$

18.

$\frac{4}{5} = \frac{x + 2}{15}$