Download Accelerated Math I - Harrison High School

CCGPS Analytic Geometry
Unit 3 Circles & Volume:
Lesson 1-Circles
1) Properties of Triangle Similarity:
a. Chords: a segment whose endpoints are on a circle or a sphere
If chords are equidistant from the center of the circle, then they are congruent.
If a radius is perpendicular to a chord it bisects the chord.
b. Tangents: a segment/line in the plane of a circle that intersects the circle
in exactly 1 point (point of tangency)
i. Perpendicular to the radius
c. Secants: a line that intersects a circle in 2 points
2) Properties of Angles:
a. Inscribed Angles: angle whose vertex is on a circle & sides are chords
b. Central Angles: angle with vertex at center of circle & sides are radii
i. Intercepted arc is the same as the angle measure
c. Other:
3) Properties of Circles:
a. Arc: a continuous part of the circle
i. Intercepted Arc: portion of a circle that is in the interior of an
inscribed angle & endpoints are on sides of angle
1. Major Arc: larger than semicircle
2. Minor Arc: smaller than semicircle
ii. Length of an Arc:
Lesson 2-Area Sector
b. Sector: the region bounded by 2 radii of the circle & the arc they intercept
i. Area of a Sector:
Lesson 3-Volume
1) Measurement:
a. Spheres:
i. The Great Circle: cross section with the diameter
ii. Effect of changing radius
1. Factor changing the radius is cubed to change the volume
b. Cylinders:
c. Pyramids:
d. Cones: