Lesson 5 Circular Reasoning Practice Understanding

Ready

Determine the angles of rotational symmetry and the number of lines of reflective symmetry for each of the polygons below.

1.

Equilateral Triangle

2.

Rectangle

3.

Rhombus

4.

Regular Hexagon

5.

Square

6.

Regular Decagon

Solve each right triangle by finding the missing angles and sides.

7.

8.

9.

10.

Set

Use Circle K for problems 11–13.

11.

Given: $m ∠ L G H$ and $m ∠ G H J$ are both $45 °$ .

a.

Find $m ∠ G M H$ .

b.

Find $m \overset{⌢}{L H}$ .

c.

Find $m ∠ L K H$ .

d.

Find $m ∠ J M L$ .

12.

$△ G K H$ has two sides that are radii of the circle.

a.

What type of triangle is $△ G K H$ ?

b.

Identify another triangle formed by two radii.

13.

Given: $m \overset{⌢}{G H} = 113.2 °$ .

a.

Find $m ∠ G K H$ .

b.

Find $m ∠ K G H$ .

c.

Find $m ∠ K H J$ .

d.

Find $m ∠ J K L$ .

e.

Find $m \overset{⌢}{J L}$ .

Use the figure for problems 14–16.

14.

Identify the right angles in $⨀ G$ . How do you know?

15.

Identify four inscribed angles with the same measure. How do you know?

16.

Given: $m ∠ G F E = 70 °$

a.

Find $m ∠ E G F$ .

b.

Find $m ∠ B F A$ .

c.

Find $m \overset{⌢}{E F}$ .

d.

Find $m \overset{⌢}{A F}$ .

e.

Find $m ∠ A C F$ .

Go

Find the indicated distances and areas.

17.

$⨀ R$ is cut by two diameters that are perpendicular to each other.

a.

Find the distance to walk along arc $N Q$ .

b.

Find the area inside one of the four sectors.

c.

Find the distance to walk along the following path: Start at point $P$ and go to $R$ then to $Q$ and over to $N$ then back to $P$ .

18.

$⨀ S$ is cut by three diameters that create equal angles at the center of the circle.

a.

Find the distance to walk along arc $U T$ .

b.

Find the area inside one of the six sectors.

c.

Find the distance to walk along the following path: Start at point $U$ go to $S$ then to $V$ then to $W$ followed by $X$ and then back to $U$ .