Bellwork 43° 88° 2x° (3x + 1)°

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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

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

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

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

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

Activity lab

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.

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

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 = 128.6 Divide each side by 7. Answer: The measure of each angle in a regular heptagon is 128.6°. Example 3

Find the measure of each angle in a regular hexagon. B. 104.2° C. 120° D. 132.8° A B C D Example 3

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

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

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

End of the Lesson End of the Lesson

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

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. 10.6 cm C. 11.7 cm D. 43.9 cm A B C D Five Minute Check 1

(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. 16.3 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

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

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