Geometry – Chapter 11 Lesson Plans
Section 11.1–Parts of a Circle
Enduring Understandings: The student shall be able to:
- Identify and use parts of circles.
Standards:
30. Circles
Identifies and defines circles and their parts (center, arc, interior, exterior); segments and lines associated with circles (chord, diameter, radius, tangent, secant); properties of circles (congruent, concentric, tangent); relationship of polygons and circles (inscribed, circumscribed); angles (central; inscribed; formed by tangents, chords, and secants).
Essential Questions: What are the different parts of a circle?
Warm up/Opener:
Activities:
Definition of a Circle: A circle is the set of all points (a locus of points) in a plane that are a given distance from a given point in the plane, called the center of the circle.
Segments of Circles:
Radius: a segment from the center of the circle to a point on the circle.
Chord: a segment whose endpoints are on the circle.
Diameter: a chord that contains the center.
Thm 11-1: All radii of a circle are congruent.
Thm 11-2: The measure of the diameter d of a circle is twice the measure of the radius r of the circle. (d = 2r)
Concentric: Two circles are concentric if they share the same center. Examples are a bulls-eye, dart board, or rings on a pond when a pebble is dropped in the still water.
Circumference: the perimeter of the circle, or the distance around a circle.
This is really Section 11.5, but it fits well here. We want to discover the relationship of circumference and diameter. Hand out circular objects and have the class measure the circumference and diameters. Then have them calculate the ratio of circumference/diameter is a little more than 3, and the exact value is.
is a non-repeating, non-terminating number, which makes it an irrational number.
Talk about the circumference is used to calculate how far a round object would roll in one revolution.
Circumference = * d = 2 * * r
We will use this information in the next section in calculating arc lengths.
Locus of points: A locus is the set of all points that satisfy a given condition or conditions. The plural for locus is loci (LOW-sigh).
- Describe the locus of points in a plane at a given distance from a fixed point in the plane.
- Describe the locus of points at a given distance, or less, from a fixed point in a plane.
- Describe the locus of points in a plane satisfying the equation y = 3x – 5
- Describe the locus of points in space at a given distance from a fixed point.
- Have the students to the exercises on page 461 on locus FOR EXTRA CREDIT
Assessments:
Do the “Check for Understanding”
CW WS 11.1 of the blue book
HW pg 457-458, # 13 - 33by fours (6)