Lessons

1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

Circles and similar figures

Objective:

• Learning and using the formulas for the circumferences and areas of circles, arc lengths and the areas of sectors of a circle.

• Finding the ratio of the areas of two triangles

• Deeper understanding of scale factors, perimeters, and areas of similar figures

• Introduction to geometric probability

Lesson 11-2 Circles and similar figures

Circumference: Perimeter of a circle

Circumference, C, of circle with radius r: C=2r

Circumference, C, of circle with diameter d: C=d

Area, A, of circle with radius r:       A=r2

Sector of a circle: A region bounded by two radii and an arc of a circle

The red region is a Sector and gray region is also a sector

Finding Length and area of a sector:

Measure of arc=X

Length of the arc= (x/360)(2r)

Area of the sector= (x/360)(r2)

The length of the arc= (x/360)(2r) =( 60/360)(25)= 5/3

The area of the sector= (x/360)(r2) = (60/360)(52) =25/6

 Theorem 11-6 If the scale factor of two similar figures is a:b, then (1) the ratio of the perimeters is a:b (2) the ratio of the areas is a2: b2

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