1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
1. How many sides does a hexagon have?
2. How many sides does a pentagon have?
3. How many angles does an octagon have?
4. Evaluate (n – 2)180 for n = 7. 6 5 8
900

3. Problem of the Day
Jeffrey planted four carnations, three dahlias, seven marigolds, five cornflowers, one geranium, and four mums. He forgot to water them and on each of the two following days, half the remaining flowers died. How many flowers were still living at the end of the second day? 6

4. Sunshine State Standards
MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180 degrees and apply this fact to find…the sum of angles in polygons.

5. Vocabulary polygon regular polygon trapezoid parallelogram rectangle
rhombus
square

6. A polygon is a closed plane figure formed by three or more segments
A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides.

7. Polygon
Number of Sides 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon n
n-gon

8. Additional Example 1A: Finding Sums of the Angle Measures in Polygons
Find the sum of the angle measures in a hexagon.
Draw diagonals to divide the figure into triangles.
4 triangles
4 • 180° = 720°

9. Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued
Find the sum of the angle measures in a octagon.
Draw diagonals to divide the figure into triangles.
6 triangles
6 • 180° = 1080°

10. Check It Out: Example 1
Find the sum of the angle measures in a heptagon.
Draw diagonals to divide the figure into triangles.
5 triangles
5 • 180° = 900°

11. The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2).
All the sides and angles of a regular polygon have equal measures.

12. Additional Example 2A: Finding the Measure of Each Angle in a Regular Polygon
Find the angle measures in the regular polygon.
8 congruent angles
8x° = 180°(8 – 2)
8x° = 180°(6)
8x° = 1080°
8x° 8
1080°8 =
x° = 135°

13. Additional Example 2B: Finding the Measure of Each Angle in a Regular Polygon
Find the angle measures in the regular polygon.
4 congruent angles
4y° = 180°(4 – 2)
4y° = 180°(2)
4y° = 360°
4y° 4
360°4 =
y° = 90°

14. Check It Out: Example 2
Find the angle measures in the regular polygon.
9 congruent angles
9y° = 180°(9 – 2)
9y° = 180°(7)
9y° = 1260°
9y° 9
1260° =
y° = 140°

15. Quadrilaterals with certain properties are given additional names
Quadrilaterals with certain properties are given additional names. A trapezoid has exactly 1 pair of parallel sides. A parallelogram has 2 pairs of parallel sides. A rectangle has 4 right angles. A rhombus has 4 congruent sides. A square has 4 congruent sides and 4 right angles.

17. Additional Example 3A: Classifying Quadrilaterals
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rectangle
4 right angles
rhombus
4 congruent sides
square
4 congruent sides and 4 right angles

18. Additional Example 3B: Classifying Quadrilaterals
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rhombus
4 congruent sides

19. Check It Out: Example 3A
Give all the names that apply to each figure.
Quadrilateral – 4 sided polygon Trapezoid – 1 pair of parallel sides

20. Check It Out: Example 3B
Give all the names that apply to each figure.
Quadrilateral – 4 sided polygon Parallelogram – 2 pairs of parallel sides Rhombus – 4 congruent sides

21. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 21

22. Lesson Quiz: Part I
1. Find the sum of the angle measures in a quadrilateral.
2. Find the sum of the angle measures in a hexagon.
3. Find the measure of each angle in a regular octagon.
360°
720°
135°

23. Lesson Quiz: Part II
4. Write all of the names that apply to the figure below.
quadrilateral, rhombus, parallelogram

24. Lesson Quiz for Student Response Systems
1. Identify the sum of the angle measures in a heptagon.
A. 520°
B. 540°
C. 720°
D. 900° 24

25. Lesson Quiz for Student Response Systems
2. Identify the sum of the angle measures in a 17-gon.
A. 1800°
B. 2700°
C. 3060°
D. 3600° 25

26. Lesson Quiz for Student Response Systems
3. Identify all the names that apply to the given figure.
A. parallelogram, rectangle
B. trapezoid, quadrilateral
C. rhombus, square, trapezoid
D. rectangle, quadrilateral, trapezoid 26