Download Holt McDougal Geometry

Developing Formulas
Circles and Regular Polygons
Warm Up
Find the unknown side lengths in each special
right triangle.
1. a 30°-60°-90° triangle with hypotenuse 2 ft
2. a 45°-45°-90° triangle with leg length 4 in.
3. a 30°-60°-90° triangle with longer leg length 3m
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
Essential Question
• What is a circle? What are the different
parts of a circle?
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
Unit 3: Circles/ Volume
• Section 1: Introduction to Circles
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
Standard(s):
• MCC9-12.G.C.2
Identify and describe relationships among
inscribed angles, radii, and chords. Include
the relationship between central, inscribed,
and circumscribed angles; inscribed
angles on a diameter are right angles; the
radius of a circle is perpendicular to the
tangent where the radius intersects the
circle.
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
As we go through this lesson
-
Fill in your graphic organizer
Write in your definitions under what is it
Write the notation under how do I write it
Label each item on the circle at the top of
the page.
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a circle
A circle is the set of all points in a plane that are the same
distance from a given point, called the center of the
circle.
A circle is named by the symbol  and its center.
How do I write it C
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is the center of the circle?
The center of a circle is a fixed point in space that is an equal distance
from every point on the circle.
How do I write it?
Based on what the point is labeled C
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is the diameter of a circle?
The distance across a circle through the
center is the diameter of the circle.
How do I write it: Based on it’s endpoints
EM
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What Is the radius of a circle?
The radius is the distance from the center of
a circle to a point on the circle.
How do I write it? Based on the end points
CD
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a chord:
A chord is a segment whose endpoints are
points on the circle
How do I write it? Based on it’s end points
AB, PF
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a central angle?
A central angle of a circle is an angle whose
sides are radii.
How do I write it?
∠ ECD, ∠ DCM
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a secant line?
A line that intersects a circle at two points is
called a secant line.
How do I write it?
NP
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a Tangent line
A tangent line of a circle is a line that
intersects the circle in exactly one point.
How do I write it?
DT
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is the point of tangency?
The point of tangency is the point at which
a tangent intersects a circle. Note:
Perpendicular to the radius
How do I write it? D
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is an arc?
An arc is an unbroken portion of a circle that
lies between two points on the circle.
How do I write it? AB measure in degrees
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a minor arc?
Two points on a circle determine a minor arc
and a major arc; the minor arc is the arc
with the lesser measure.
How do I write it? PF
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a major arc?
• Two points on a circle determine a minor
arc and a major arc; the major arc is the
arc with the greater measure.
• How do I write it? PEF
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is a semi circle?
A semi circle is an arc whose endpoints
form the endpoints of a diameter of the
circle.
How do I write it? EM
Holt McDougal Geometry
Developing Formulas
Circles and Regular Polygons
What is an inscribed angle?
• An angle whose vertex is on a circle and
whose sides contain chords of the circle is
an inscribed angle.
• How do I write it? ∠ NPF
Holt McDougal Geometry