Download 10.2 Polygons

10.2 Polygons
A plane figure is an object in a plane.
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 3
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 4
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 5
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 7
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 8
Polygons
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 9
Polygons and Angles
• Example: Find the sum of the
measures of the interior angles
in ΔABC.
Polygons and Angles
• Example: Find the sum of the
measures of the interior angles
in ΔABC.
• Solution: Construct line m containing line
segment AC and a second line l through point
B parallel to m.
(continued on next slide)
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 10
Polygons and Angles
m∠1 = m∠ 4 (alternate interior angles)
m∠ 3 = m∠ 5 (alternate interior angles)
m∠ 1 + m∠ 2 + m∠ 3
= m∠ 4 + m∠ 2 + m∠ 5
= 180°
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 12
Polygons and Angles
• Example: Find the interior
angle sum of the convex
pentagon ABCDE.
Polygons and Angles
• Example: Find the interior
angle sum of the convex
pentagon ABCDE.
• Solution: Divide the
pentagon into a collection of
triangles.
(continued on next slide)
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Section 10.2, Slide 14
Polygons and Angles
=
=
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Section 10.2, Slide 15
Draw a hexagon.
How many triangles does it break up into?
What is the sum of the interior angles?
A convex polygon with n sides can be
broken down into (n-2) triangles.
The sum of the angles in a triangle is 180o.
In a regular polygon you have n equal sides
and n equal angles. So for each angle...
Polygons and Angles
• Example: A billboard is to be in the shape of a
giant star. Determine the angle measure of each
point of the star.
(continued on next slide)
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 19
Polygons and Angles
• Solution:
Pentagon angles:
A straight angle
equals 180°, ∠EZV
and ∠EVZ each
have measure 72°.
∠E has measure
180° – 72° – 72° = 36°.
(continued on next slide)
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 21
Similar Polygons
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Section 10.2, Slide 22
If one object is a scaled, rotated, and even
flipped version of another, then they are
similar.
b
y
a
z
c
x
If two objects are similar, ratios of similar
edges are equal.
a b c
= =
x y z
Similar Polygons
• Example: A bridge is to be used to cross a
river. The distances in the two right triangles
were measured. Use this information to find the
distance, d, across the river.
(continued on next slide)
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 23
Similar Polygons
• Solution:
m∠BAC = m∠ DAE (vertical angles)
m∠ C = m∠ D = 90° (right angles)
ΔACB is similar to ΔADE
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.2, Slide 24