Polygons, Circles, and Angles

Classifying Polygons

• Polygon—closed figure with at least 3 sides

• Regular polygon—all sides and angles are congruent

Classifying Polygons cont…

• Triangles are classified by sides and angles– Sides• Scalene• Isosceles• Equilateral

– Angles• Right• Obtuse• Acute

Classifying Angles cont…

• Quadrilaterals—4 sided figures– Trapezoid- 1 pair of parallel sides– Parallelogram- 2 pairs of parallel sides• Rhombus- 4 congruent angles• Rectangle- 2 sets of parallel sides and 4 congruent

angles• Square- all parallel sides and 4 congruent angles

Formula for measure of angles

• Finding total measure of angles in a polygon

• S = 180 (n – 2)N- number of sidesS- measure of angles

*the reason for 180 is because any figure can be divided into triangle

Circles

• Circle- set of all points that are the same distance from the center

• ∏= 3.14• Circumference –distance around a circle

C = ∏dC = 2r∏

Circles cont…

Radius ½ the diameter

Diameter

Chord

Making Circle Graphs

• Set up a proportion to find the measures of the central angles– The amount of degree in a circle is 360– The sum of the all percents should equal 100• The percent amount goes over 100• The missing angle goes over 360

Making Circle Graphs cont…

• Ex: Monthly Budget– Recreation – 20%

– Food- 25%

– Clothes- 15%

– Savings- 40%

Making Circle Graphs cont…

Making Circle Graphing cont…

• When the numbers aren’t in percents, add to find a total– Set up ratio as part to whole– Set up proportion to find the measures of the

central angles• Remember the missing angle is over 360• The other side of the proportion is the ratio

Making Circle Graphs cont…• Ex: Kentucky’s National Parks (millions of people visited)

Lincoln’s Birthplace – 0.3

Big South Fork – 0.4

Cumberland Gap – 1.3

Mammoth Cave – 1.8Total =

Making Circle Graphs cont…

Angle Relationships

• Supplementary—add up to 180• Complementary—add up to 90

Angle Relationships cont…

• Adjacent angles—share a vertex and a side but have no interior points in common– supplementary or complementary

1 4 2

3

Angle Relationships cont…

• Vertical angles—formed by 2 intersecting lines and are opposite each other– Alternate interior—are vertical angles that are

INSIDE the intersecting lines– Alternate exterior—are vertical angles that are

OUTSIDE the intersecting lines 1 4 2 3

Angle Relationships cont…

• Transversal—line that intersects 2 other parallel lines in different points

• Corresponding angles—lie on the same side of the transversal line and alternate

1 2 3 4

5 67 8

Angle Relationships cont…

line A1 2

line B 3 4

5 67 8 line C

Congruent Figures

• Congruent Figures—have the same size, shape, and their corresponding parts have equal measures– This is used to find missing amounts in diagrams

Congruent Figures cont…

D 50 m 30 m

B 40 m C E

A

Identifying Congruent Triangles

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

Transformations

• Transformation—change of position or size of a figure

• 3 types– Translation– Reflection– Rotation

Transformations cont…

• Translation—slide– Same distance and direction for all points moved– Figure stays the same shape• First translate each vertex of the figure• Connect the image points• The image is congruent to the original figure

Transformations cont…

• Translations cont…– To find the coordinates of a translated image, add

or subtract the # of units moved from the coordinates of the original figure

– Ex: (-4,3) (-2,-1)– Ex: (3, -5) (4,-3)

Transformations cont…

• Reflection—flips a figure over a line of symmetry– Line of symmetry—divides a figure into 2

congruent halves and is a mirror image of the other half• Reflecting over the x-axis—changes the y numbers only• Reflecting over the y-axis—changes the x numbers only• Figures can also be reflected across any line in the

plane

Transformations cont…

• Rotation—turn about a fixed point– Angle of rotation—angle that measures the

amount of the rotation (90°, 180°, 270°, 360°)– Rotational symmetry—if you can rotate a figure

180° or less and match the original figure• Divide 360 by the number of points in the figure