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Name: Chanhee Kim
Subject/Grade Level: Math/ 9th -12th
Unit: Chapter 5 Discovering and Proving Polygon Properties
Lesson Title: 5.1 Polygon Sum Conjecture
Date
Rationale: I will focus students understanding Polygon sum conjecture by using triangle
sum theorem. Students are going to draw triangles and count the number of triangles in
a polygon and figure out the relationship between the number of triangles and the
number of sides of the polygon.
Objectives: Students will be able to
- Discover a formula for finding the sum of the angle measures for n-gon
- Use deductive reasoning to explain how the polygon sum formula works
Relevant Goals:
- Review and use the algebraic skills
- Review geometric terms and properties (parallel, right angle, polygon, regular polygon,
quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon…)
- Review and use triangle sum conjecture
Essential Questions: How many triangles can be formed if you draw a line from a
vertex by connecting two non adjacent vertices in a polygon? Is there any relationship
between the number of triangles formed inside the polygon and the number of sides of
the polygon?
Assessment of learning: Students’ responses during lecture will give me idea about
how much they understand the conjecture. Homework completion will also provide me
with the feedback regarding how much students understand the triangle properties.
Instructional Strategies
* Warm up: 10 min.
- Warm up problems
- Solve
* Exploration and activity: 15 min.
- Group Activities: connect two non adjacent vertices from a vertex of the polygon and
find out the relationship between the number of sides of the polygon and the number of
the triangles.
- Figure out the sum of the angles of the polygon using the triangle sum theorem.
* Instruction: 15 min
- Investigate and compare the result of the activity
- Quadrilateral sum conjecture: The sum of the measures of the four angles
of any quadrilateral is (180 x 2)º
- Pentagon Sum Conjecture: The sum of the measures of the five angles of
any pentagon is (180 x 3)º
- Polygon Sum conjecture: The sum of the measures of the n interior angles
of an n-gon is
S
* Example problems: 5 min.
a. The polygon has seven sides
angle sum = 180° x 5, or 900°
all the angles have the same measure
measure of an angle is 900°/ 7 = 128.6°.
b. The polygon has five sides
the angle sum is 180°x 3, or 540°
90° + 120° + 110° + 95° + t = 540°
t= 125°.
* Closure: 5 min.
- Summarize: Polygon sum conjecture ( Interior angle Sum = ( n – 2 ) x 180 )
- home work: p.259-260 #3 ~ #14 Work individually and finish at home
Materials/Preparation Needed: Textbook, whiteboard, marker, doc cam, teacher’s
note, computer and activity work sheet.
Warm-up Problems
Geometry
Date
1. Find the angle measure
2. Complete the congruence statement and tell which congruence conjecture supports
the congruence statement.
`
.
Group Activity
Geometry
5.1 Polygon Sum Conjecture
Draw all the diagonals from the vertex A of your polygon. How many triangles does the diagonal
create? Can you calculate sum of all the interior angles of the created triangles without
protractor?
1.
Number of the sides of the polygon
Number of triangles created
Sum of measures of interior angles of all the
triangles
A
2.
Number of the sides of the polygon
Number of triangles created
Sum of measures of interior angles of all the
triangles
A
3.
Number of the sides of the polygon
Number of triangles
Sum of measures of interior angles of all the
triangles
A
4. If there is a n-gon (polygon with n sides), can you estimate how many triangles you
can create by drawing from a vertex in the n-gon? Calculate the sum of measures of all
the interior angles
Example Problems
Find the lettered angle measures.
a.
b.