1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
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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