Download Chapter 10 Introducing Geometry

6/8/2011
Review of Ideas about Segments,
Angles, and Triangles
Chapter 10
Introducing Geometry
Section 10.3
More about Angles
In small groups, complete the MiniMiniInvestigation on the next slide.
B sure tto use appropriate
Be
i t symbols
b l when
h
naming each.
Angles in Intersecting Lines
Transversal
Interior ∟s
Exterior ∟s
Corresponding ∟s
Same--Side Interior ∟s
Same
Same--Side Exterior ∟s
Same
Angles Formed By a Transversal
Activity
Draw two coplanar, nonnon-parallel lines that
are intersected by a transversal.
Identify the special angle pairs.
Find the measure of each angle
angle.
Repeat the activity, but draw two parallel
lines that are intersected by a transversal.
What do you notice about the special
angle pairs?
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Angle Congruencies
in Parallel Lines
Angles in Polygons
Consider two lines cut by a transversal.
If the lines are parallel, then…
– the corresponding angles are congruent.
– the alternate interior angles are congruent.
– the alternate exterior angles are congruent.
– the samesame-side interior angles are supplementary.
– the samesame-side exterior angles are supplementary.
Polygon Angle Investigation
# Sides Polygon
# of Triangles
in Polygon
Sum of
Interior
Angles
Sum of
Exterior
Angles
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Angle Sum for Triangles
The sum of the measures of the interior
angles of a triangle is 180°
180°.
Angle Sum for Quadrilaterals
The sum of the measures of the interior
angles of a quadrilateral is 360°
360°.
Angle Sums in Polygons
Angle Sum for Any Polygon
The sum of the interior angles of an n-gon
is (n
(n – 2) 180°
180°.
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5
6
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Exterior Angle Sum for Any Polygon
The sum of the exterior angles of any
polygon is 360
360°°.
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Angles in Regular Polygons
Interior Angle Measure for a Regular Polygon
The measure of each interior angles of a regular
n-gon is (n – 2) 180
180°°
n
Exterior Angle Measure for a Regular Polygon
The measure of an exterior angle of a regular
n-gon is 360°
360°
n
Central Angle Measure for a Regular Polygon
The measure of a central angle of a regular
n-gon is 360°
360°
n
Examples
Find the measure of each exterior
angle of a regular hexagon.
Find the measure of the interior angle
of a regular dodecagon.
A pizza is cut into 8 equal slices. Find
the measure of the angle formed by
the sides of a slice of pizza.
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Circles and Angles Activity
Draw a circle and label the center C.
Draw two radii, CA and CB.
Draw two chords, AD and BD.
Draw two secant segments, AF and BF.
Find the measure of the following:
– ∟ACB
– ∟ADB
– ∟AFB
Angles in Circles
Location of
Angle Measure
Vertex
Center of
∟ = intercepted arc measure
Circle
On Circle
What relationships can be determined between
the angles and their intercepted arcs?
Interior of
Circle
Exterior of
Circle
∟= ½ intercepted arc measure
∟= ½ (sum of intercepted arcs)
∟= ½ (difference of intercepted arcs)
Extra Practice
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