1. Bellwork
43°
88°
2x°
(3x + 1)°

2. Splash Screen

3. regular polygon – has all sides and angles are congruent
Classify polygons and determine which polygons can form a tessellation.
Polygon - a simple closed figure formed by three or more straight line segments.
regular polygon – has all sides and angles are congruent
Pentagon - 5 sides
Hexagon – 6 sides
Heptagon – 7 sides
Octagon – 8 sides
Nonagon – 9 sides
Decagon – 10 sides
Tessellation – a repetitive pattern of polygons that fit together with no overlaps or holes.
Main Idea/Vocabulary

4. Answer: The figure is not a polygon since it has a curved side.
Classify Polygons
Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.
Answer: The figure is not a polygon since it has a curved side.
Example 1

5. C. not a polygon, sides overlap D. not a polygon, closed figure
Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.
A. polygon, regular
B. pentagon, not regular
C. not a polygon, sides overlap
D. not a polygon, closed figure A B C D
Example 1

6. Classify Polygons
Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.
Answer: This figure has 6 sides which are not all of equal length. It is a hexagon that is not regular.
Example 2

7. C. not a polygon, sides overlap D. not a polygon, closed figure
Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.
A. polygon, regular
B. polygon, not regular
C. not a polygon, sides overlap
D. not a polygon, closed figure A B C D
Example 2

8. Activity lab

9. The number of triangles is 2 less than the number of sides.
pentagon
heptagon
rectangle
hexagon 4 5 6 7 2 3 4 5
360°
540°
720°
900°
You add 180° for every side.
The number of triangles is 2 less than the number of sides.
(n- 2)•180°
Since a regular polygon has all the same angles, you would divide the total by how many angles there are.

10. Angle Measures of a Polygon
ALGEBRA Find the measure of each angle of a regular heptagon. Round to the nearest tenth of a degree.
Draw all of the diagonals from one vertex and count the number of triangles formed.
Example 3

11. Angle Measures of a Polygon
Find the sum of the measures of the polygon.
number of triangles formed × 180°
sum of angle measures in polygon =
5 × 180°
900° =
Find the measure of each angle of the polygon. Let n represent the measure of one angle in the heptagon.
7n = 900 There are seven congruent angles.
n = Divide each side by 7.
Answer: The measure of each angle in a regular heptagon is 128.6°.
Example 3

12. Find the measure of each angle in a regular hexagon.
B °
C. 120°
D ° A B C D
Example 3

13. The measure of each angle in a regular hexagon is 120°.
PATTERNS Ms. Pena is creating a pattern on a wall. She wants to use regular hexagons. Can Ms. Pena make a tessellation with regular hexagons?
The measure of each angle in a regular hexagon is 120°.
The sum of the measures of the angles where the vertices meet must be 360°. So, solve 120n = 360°. . .
n = 3
Example 4

14. Answer:. Since 120° divides evenly into 360°, the
Answer: Since 120° divides evenly into 360°, the regular hexagon can be used.
Interactive Lab:
Tessellations
Example 4

15. QUILTING Emily is making a quilt using fabric pieces shaped as equilateral triangles. Can Emily tessellate the quilt with these fabric pieces?
A. yes
B. no A B
Example 4

16. End of the Lesson
End of the Lesson

17. Five-Minute Check (over Lesson 10–7) Image Bank Math Tools
Tessellations
Translations
Resources

18. Find the value of x in the pair of similar figures.
(over Lesson 10-7)
Find the value of x in the pair of similar figures.
A. 6.7 cm
B cm
C cm
D cm A B C D
Five Minute Check 1

19. (over Lesson 10-7)
Caren’s dollhouse furniture is made to scale of real furniture with a ratio of inch to 1 foot. If a dollhouse table is 3.4 inches wide and 4.2 inches long, what are the dimensions of the “real” table from which it was modeled?
A ft by 20.1 ft
B. 8.8 ft by 7.1 ft
C. 8.5 ft by 10.5 ft
D. 1.4 ft by 1.7 ft A B C D
Five Minute Check 2

20. Which statement is true?
(over Lesson 10-7)
Which statement is true?
A. All squares are similar.
B. All rectangles are similar.
C. All right triangles are similar.
D. All acute triangles are similar. A B C D
Five Minute Check 3

21. End of Custom Shows