Transcript  Some sequences of geometric objects change in predictable ways.  Some angles have special relationships based on their position or measure.  Polygons can be described.


Some sequences of geometric objects
change in predictable ways.

Some angles have special relationships
based on their position or measure.

Polygons can be described uniquely by
their sides and angles.
Draw a triangle on a piece of paper.
 Find the measure of each of the 3 angles
in your triangle.
 Compare your angle measures with
those of your table group. What
patterns or relationships do you observe?


Other than by measuring, how could we
prove that the measures of the angles in
a triangle add up to 180o?
Draw a triangle on a notecard.
 Cut out the triangle.
 Label each vertex of the triangle (close
to the vertex)
 Cut off the vertices of the triangle.
 Put them together.
 What do you get?


Use the Parallel Postulate (p. 604)
› Look at figure 10.22 on p. 605
What do we know?
 What does this tell us?

A
l
m
4
1
B
2
5
Line l is
parallel to
line m
3
C
Draw a triangle on a piece of paper.
 What is the sum of the angle measures of
the 3 exterior angles in your triangle?

1
2
Compare your results with those of your
table group, and make a conjecture.
 How could you prove your conjecture?


On a post-it, write a conjecture for what
you think the rule might be for finding the
measure of the exterior angles of any
polygon.

How might you prove your conjecture?

Method 1: Cut out exterior angles

Method 2: Walk-and-Turn
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Method 3: Use the relation with the sum
of the interior angles
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Quadrilaterals
› In your groups, draw a quadrilateral.
› Measure each angle.
› Find the sum of the angle measures.
› Record your result.

Repeat with a polygon with more than 4
sides.
Sides
Total Angle Measure
Avg. Angle Measure
3
180°
60°
4
5
6
7
8

What pattern(s) do you notice?

What conjecture can you make?

How could you prove your conjecture?

There are 3 approaches for determining
the measure of the interior angles of a
polygon:
› Find the triangles with a common vertex at
one vertex of the polygon
› Find the triangles with a common vertex in
the center of the polygon
› Walk and Turn
Section 10.3: #’s 15, 16, 22, 41, 42, 43, 47,
49
 Turn in #’s 15, 16, 42, & 47
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