Lesson 2 Circle Dilations Solidify Understanding

Ready

Find the missing angle(s) in each of the figures.

1.

Triangle with two angles 93, 65, and x degrees

2.

Triangle with one angle x and two exterior angles of 125 and 83 degrees.

3.

Two triangles that share a common side. One triangle has angles 40,30, and x. The other triangle has angles y, 40, and 100.

4.

Triangle divided into two triangles by an altitude; angles labeled q, r, s, and 35 degrees.

Find the angle of rotational symmetry for each regular polygon. (Note: A figure has rotational symmetry if it can be rotated by an angle between and so that the image coincides with the pre-image. The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself.)

5.

Regular pentagon

6.

Regular octagon

Set

7.

Circle A with orange dashed circle around it, Blue Circle K
  • If and are similar, locate the center of dilation.

  • If the black, solid circle and the red, dotted circle are similar, locate the center of dilation.

  • Which of the circles in the figure are similar? Justify your answer.

The radii for each of the circles in Figure 2 are , , and .

Circle A with radius AC and orange dashed circle circumscribed with radius AD. Blue Circle B with radius BP. Figure 2

8.

What is the scale factor that dilates the circle with radius to the circle with radius ?

9.

What is the scale factor that dilates black, solid to ?

10.

If the circumference of black, solid is , what is the circumference of ?

Go

Construct the line of reflection between the image and the pre-image. Then write the equation of the line of reflection.

11.

Triangle ABC A(-1,-1) B(-1,-3), C(-3,-3). Triangle A'B'C' A'(0,0) B'(2.0), and C'(2,2) x–3–3–3–2–2–2–1–1–1111222y–3–3–3–2–2–2–1–1–1111222000

Equation:

12.

Triangle PQR P(0,4), Q(3,2) R(-2.0) Triangle P'Q'R' with P'(0,4) Q(2,1) and R(.5,.5). –2–2–2222222444000

Equation:

13.

Draw the radius of the circle. (Note: The definition of radius requires you know or can locate the center of the circle. Construct the center before you draw the radius.)

A Circle

14.

Draw the diameter of the circle. (Note: The definition of diameter requires you know or can locate the center of the circle. Construct the center before you draw the diameter.)

A Circle