DISCOVERING GEOMETRYCHAPTER 5

Lesson 1: 5.1 and 5.2Lesson 2: 5.3Lesson 3: 5.4Lesson 4: 5.5Lesson 5: 5.6Lesson 6: 5.7Lesson 7: Review

Warm-Up

List the numbers from 3 to 10, followed by the name of the polygon that has that many sides. Example:

3 – triangle 8 -4 - 9 -5 - 10 -6 -7 -

5.1 and 5.2 – Polygon Angle Sums

INVESTIGATION– Draw a pentagon.

– Draw all of the diagonals from ONE vertex in your pentagon.How many triangles did you create?

– What is the sum of the interior angles in each triangle?

– What is the sum of the interior angles in the pentagon?

– If the pentagon is REGULAR, what is the measure of EACH interior angle?

Investigation

– Draw a hexagon.

– Draw all of the diagonals from ONE vertex in your pentagon.How many triangles did you create?

– What is the sum of the interior angles in each triangle?

– What is the sum of the interior angles in the pentagon?

– If the pentagon is REGULAR, what is the measure of EACH interior angle?

5.1 and 5.2 – Polygon Angle Sums

CONJECTURE: Polygon Sum– The sum of the measures of the n interior angles

of an n-gon is __________.

# of Sides

# of Diagonals from one vertex

Sum of the Interior Angles

3456n

5.1 and 5.2 – Polygon Angle Sums

5.1 and 5.2 – Polygon Angle Sums

DEMONSTRATION: Exterior Angles Activity 5.2

5.1 and 5.2 – Polygon Angle Sums

CONJECTURE: Exterior Angle Sum– For any polygon, the sum of the measures of a

set of exterior angles is _________.

– IF THAT POLYGON IS REGULAR, then each exterior angle measures _________.

5.1 and 5.2 – Polygon Angle Sums

EXAMPLES– Consider an octagon.

What is the sum of its INTERIOR angles?

What is the sum of its EXTERIOR angles?

– Now suppose that the octagon is REGULAR. What is the measure of EACH INTERIOR angle?

What is the measure of EACH EXTERIOR angle?

5.1 and 5.2 – Polygon Angle Sums

EXAMPLES– How many sides does a regular polygon have if

each exterior angle measures 24°?

– How many sides does as polygon have if the sum of its interior angle measures is 7380°?

Ticket out the door

1. How many sides does a regular polygon have if each exterior angle measures 40°?

2. How many sides does a polygon have if the sum of its interior angle measures is 2160°?

3. How many sides does a regular polygon have if each interior angle measures 140°?

4. How many sides does a polygon have if the sum of its interior angle measures is 2700°?

5. How many sides does a polygon have if the sum of its exterior angle measures is 360°?

Homework

Worksheets 5.1 and 5.2