A segment that joins two nonconsecutive vertices of a polygon is called a diagonal. Polygon PQRST has two diagonals from vertex R, RP &* and RT&*.


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1 age of 6 6. olygons Goal Identify and classify polygons. Find angle measures of quadrilaterals. Each traffic sign below is an example of a polygon. Notice that each sign is formed with straight lines. Key Words polygon side of a polygon vertex of a polygon diagonal of a polygon Student Help VOULY TI side connects consecutive vertices. diagonal connects nonconsecutive vertices. polygon is a plane figure that is formed by three or more segments called sides. Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon. Two vertices that are the endpoints of the same side are called consecutive vertices. For example, in polygon QST, and S are consecutive vertices. segment that joins two nonconsecutive vertices of a polygon is called a diagonal. olygon QST has two diagonals from vertex, &* and T&*. diagonals T vertex side vertex S T S EXMLE Identify olygons Is the figure a polygon? Explain your reasoning. a. b. c. d. Solution a. Yes. The figure is a polygon formed by four straight sides. b. No. The figure is not a polygon because it has a side that is not a segment. c. No. The figure is not a polygon because two of the sides intersect only one other side. d. Yes. The figure is a polygon formed by six straight sides. 6. olygons 0
2 age of 6 lassifying olygons You can classify polygons by the number of sides they have. Some special types of polygons are listed below. Student Help STUY TI To classify a polygon not listed in the table, use the number of sides. For example, a polygon with 4 sides is a 4gon. polygon with n sides is an ngon. TYES OF OLYGONS Triangle Quadrilateral entagon sides 4 sides 5 sides Hexagon Heptagon Octagon 6 sides 7 sides 8 sides EXMLE lassify olygons ecide whether the figure is a polygon. If so, tell what type. If not, explain why. a. b. c. d. Solution a. The figure is a polygon with four sides, so it is a quadrilateral. b. The figure is not a polygon because it has some sides that are not segments. c. The figure is a polygon with five sides, so it is a pentagon. d. The figure is not a polygon because some of the sides intersect more than two other sides. Identify and lassify olygons ecide whether the figure is a polygon. If so, tell what type. If not, explain why hapter 6 Quadrilaterals
3 age of 6 Quadrilaterals diagonal of a quadrilateral divides it into two triangles, each with angle measures that add up to 80. So, the sum of the measures of the interior angles of a quadrilateral is 80, or ma ma ma ma4 ma5 ma6 80 THEOEM 6. Quadrilateral Interior ngles Theorem Words The sum of the measures of the interior angles of a quadrilateral is 60. Symbols ma ma ma ma Student Help EXMLE Find ngle Measures of Quadrilaterals STUY TI Name a polygon by listing its vertices consecutively in either direction. Two names for the quadrilateral in Example are QS and QS. Find the measure of as. Solution Use the fact that the sum of the measures of the interior angles of a quadrilateral is 60. ma maq ma mas mas S Quadrilateral Interior ngles Theorem Substitute angle measures. 0 mas 60 mas 40 Simplify. Subtract 0 from each side. NSWE The measure of as is 40. Find ngle Measures of Quadrilaterals Find the measure of a olygons 05
4 age 4 of 6 6. Exercises Guided ractice Vocabulary heck. What type of polygon has 8 sides? 5 sides?. Use the diagram of the pentagon shown at the right. Name all of the diagonals from vertex. E Skill heck Is the figure a polygon? Explain your reasoning Find the measure of a ractice and pplications Extra ractice See p lassifying olygons ecide whether the figure is a polygon. If so, tell what type. If not, explain why Homework Help Example : Exs. 8 0 Example : Exs. 8 0,, 4 7 Example : Exs. 5 0, 8. Logical easoning What is the fewest number of sides a polygon can have? Explain your answer, then name the polygon. Visualize It!. Two different pentagons Sketch the figure(s) described.. hexagon with three diagonals drawn from a single vertex 4. quadrilateral with two obtuse angles 06 hapter 6 Quadrilaterals
5 age 5 of 6 Finding ngle Measures Find the measure of a IStudent Help I L S S Z O N E. O M HOMEWOK HEL Extra help with problem solving in Exs. 8 0 is at classzone.com Using lgebra Find the value of x (x 0) x 00 x 84 x arachutes Some gym classes play games using parachutes that look like the polygon below.. Tell how many sides the polygon has and what type of polygon it is.. olygon LMNQST is one name for the polygon. State two other names using the vertices. T S L M N lants. Name all of the diagonals that have vertex M as an endpoint. Not all of the diagonals are shown. lants Use the following information. ross sections of roots and stems often resemble polygons. Next to each cross section is the polygon it resembles. Tell how many sides each polygon has and tell what type of polygon it is. Source: The History and Folklore of North merican Wildflowers 4. Virginia Snakeroot 5. araway MOL, or star fruit, has a cross section shaped like a fivepointed star. 6. Fennel 7. oison Hemlock 6. olygons 07
6 age 6 of 6 8. Technology Use geometry software to draw a quadrilateral. Measure each interior angle and calculate the sum. What happens to the sum as you drag the vertices of the quadrilateral? Standardized Test ractice 9. MultiStep roblem Envelope manufacturers fold a speciallyshaped piece of paper to make an envelope, as shown below. 4 a. How many sides are formed by the outer edges of the paper before it is folded? Name the type of polygon. b. Tell how many sides are formed by the outer edges of the paper in Steps 4. Name the type of polygon formed after each step. c. If the four angles of the red quadrilateral in Step 4 are congruent, then what is the measure of each angle? Mixed eview Line elationships etermine whether the lines are parallel, perpendicular, or neither. (Lesson.) 0. ^&*( and E ^&*(. ^&*( and ^&*(. ^&*( and E ^&*(. ^&*( and E ^&*( E Finding ngle Measures Find the measure of the numbered angle. (Lesson.4) lgebra Skills istributive roperty Use the distributive property to rewrite the expression without parentheses. (Skills eview, p. 67) 7. 4(x ) 8. (x )6 9. (x 7) 08 hapter 6 Quadrilaterals 40. 5(x ) 4. (5x ) 4. (4x 4)x
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