# Geo.7 Circles

### Lesson 1

- I know what chords, arcs, and central angles are.

### Lesson 2

- I can use the relationship between central and inscribed angles to calculate angle measures and prove geometric theorems.
- I know that an inscribed angle is half the measure of the central angle that defines the same arc.

### Lesson 3

- I can use the relationship between tangent lines and radii to calculate angle measures and prove geometric theorems.
- I know that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency.

### Lesson 4

- I can prove a theorem about opposite angles in quadrilaterals inscribed in circles.

### Lesson 5

- I can construct the circumscribed circle of a triangle.
- I can explain why the perpendicular bisectors of a triangle’s sides meet at a single point.

### Lesson 6

- I can explain why the angle bisectors of a triangle meet at a single point.
- I know any point on an angle bisector is equidistant from the rays that form the angle.

### Lesson 7

- I can construct the inscribed circle of a triangle.

### Lesson 8

- I can calculate lengths of arcs and areas of sectors in circles.

### Lesson 9

- I can gather information about a sector to draw conclusions about the entire circle.

### Lesson 10

- I know that when a circle is dilated, some ratios, like the ratio of the circumference to the diameter, stay constant.

### Lesson 11

- I know that the radian measure of an angle whose vertex is the center of a circle is the ratio of the length of the arc defined by the angle to the circle’s radius.

### Lesson 12

- I understand the relative sizes of angles measured in radians.

### Lesson 13

- I can calculate the area of a sector whose central angle measure is given in radians.
- I know that the radian measure of an angle can be thought of as the slope of the line $\ell=\theta \boldcdot r$.

### Lesson 14

- I can use properties of circles to solve geometric problems.