Chapter Seven:  
Area

Geometry   Notes

Chapter  7

Section  7.1
Section  7.2
Section  7.3
Section  7.4
Section  7.5
Section  7.6
Section  7.7
Section  7.8

Geometry Contents

Take notes on the following topics.

Section 7-6  Circles and Arcs

Vocabulary

Circle (p. 386) A circle is the set of all points in a plane that are a given distance, the radius, from a given point, the center

Congruent circles (p. 386) Congruent circles are circles whose radii are congruent.

Diameter of a circle (p. 386) A diameter of a circle is a segment that contains the center of the circle and whose endpoints are on the circle. The term diameter can also mean the length of this segment.

Central angle of a circle (p. 386) A central angle of a circle is an angle whose vertex is the center of the circle.

Semicircle (p. 387) A semicircle is half a circle.

Minor arc (p. 387) A minor arc is smaller than a semicircle.

Major arc (p. 387) A major arc of a circle is an arc that is larger than a semicircle.

Adjacent arcs (p. 387) Adjacent arcs are on the same circle and have exactly one point in common.

Circumference (p. 388) The circumference of a circle is the distance around the circle. Given the radius r of a circle, you can find its circumference C by using the formula C = 2πr.

Pi (p. 388) Pi (π) is the ratio of the circumference of any circle to its diameter. The number π is irrational and is approximately 3.14159.

Concentric circles (p. 388) Concentric circles lie in the same plane and have the same center.

Arc length (p. 389) The length of an arc of a circle is the product of the ratio (degree measure of the arc)/360 and the circumference of the circle.

Congruent arcs (p. 389) Congruent arcs are arcs that have the same measure and are in the same circle or congruent circles.

 

Postulate 7-1 (Arc Addition Postulate)

The sum of the measures of two adjacent arcs is the measure of the arc formed by the adjacent arcs.

Theorem 7-13 (Circumference of a Circle)

The  circumference of a circle is π times the diameter or two times the product of π and the radius.  

Theorem 7-14 (Arc Length)

The length of an arc of a circle is the product of the ratio (degree measure of the arc)/360  and the circumference of the circle.