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

Equilateral Triangle

2.

Rectangle

Rectangle

3.

Rhombus

Rhombus

4.

Regular Hexagon

regular Hexagon

5.

Square

Square

6.

Regular Decagon

Regular Decagon

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

7.

Triangle ABC with angle C = 60 degrees and hypotenuse 1 in.

8.

Triangle FEG with angle E = 18 degrees and opposite side 2 m.

9.

Triangle JKL with angle J = 67.5 degrees and hypotenuse 5 ft.

10.

Triangle PQR with one leg 8cm and hypotenuse 10cm.

Set

Use the figure for problems 11–13.

Circle K with Inscribed angle LGH and angle JHG.

11.

Given: and are both .

a.

Find .

b.

Find .

c.

Find .

d.

Find .

12.

has two sides that are radii of the circle.

a.

What type of triangle is ?

b.

Identify another triangle formed by two radii.

13.

Given: .

a.

Find .

b.

Find .

c.

Find .

d.

Find .

e.

Find .

Use the figure for problems 14–16.

Circle G with inscribed angles ABF, ACF, ADF, AEF

14.

Identify the right angles in . How do you know?

15.

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

16.

Given:

a.

Find .

b.

Find .

c.

Find .

d.

Find .

e.

Find .

Go

Find the indicated distances and areas.

17.

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

Circle R with diameters NP and OQ. RP=6

a.

Find the distance to walk along arc .

b.

Find the area inside one of the four sectors.

c.

Find the distance to walk along the following path: Start at point and go to then to and over to then back to .

18.

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

Circle S with chords WT, VY, UX with ST=10

a.

Find the distance to walk along arc .

b.

Find the area inside one of the six sectors.

c.

Find the distance to walk along the following path: Start at point go to then to then to followed by and then back to .