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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 sides
S- 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 = ∏d
C = 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 – 1.8
Total =
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
6
7 8
Angle Relationships cont…
1
3
line B
5
7
line A
2
4
6
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…
50 m
B
A
40 m
C
D
30 m
E
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