# Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship.

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1 10-7 Quadrilaterals MAIN IDEA I will classify quadrilaterals and find missing angle measures in quadrilaterals. New Vocabulary quadrilateral rectangle square ogram trapezoid Hands-On Mini Lab The figure below is a quadrilateral, since it has four sides and four angles. Step 1 Draw a quadrilateral. Step 2 Pick one vertex and draw a segment to the opposite vertex. 1. How many triangles were formed? 2 2. Use the relationship among the angle measures in a triangle to find the sum of the angle measures in a quadrilateral. Explain. 360 ; 2(180 ) = 360 The angles of a quadrilateral have a special relationship. KEY CONCEPT Angles of a Quadrilateral Words Model w x z y The sum of the measures of the angles of a quadrilateral is 360. Symbols w + + y + z = 360 EXAMPLE Find Angle Measures 1 Algebra Find the value of x in the quadrilateral. Since the sum of the angle measures in a quadrilateral is 360, x = x = 360 Write the equation. x = 360 Add 65, 85, and = Subtract 240 from each side. x = 120 Simplify. So, the value of x is Chapter 10 Geometry: Angles and Polygons

2 Reading Math Congruent Angles The red arcs show angles. KEY CONCEPT Quadrilateral Figure Characteristics Rectangle Square Parallelogram Rhombus Trapezoid All angles are right angles All sides Classifying Quadrilaterals All angles are right angles Opposite angles All sides Opposite angles Exactly one pair of opposite sides Real-World EXAMPLE Classify Quadrilaterals 2 Classify the quadrilaterals labeled 1 and 2 in the quilt piece. Figure 1 is a square. Figure 2 is a. 1 2 Extra Examples at ca.gr5math.com Lesson 10-7 Quadrilaterals 559

3 EXAMPLE Find Angle Measures 3 What is the value of x in the ogram at the right? You know that in a ogram, opposite angles are. Since the angle opposite the missing measure has a measure of 70, x = 70. Check = Personal Tutor at ca.gr5math.com Algebra Find the value of x in each quadrilateral. See Example 1 (p. 558) The first figure is a rectangle. The 5. Classify each quadrilateral. See Example 2 (p. 559) second figure is a square Safari Stereo created the logo shown below for use in their new C13-12P A.ai C13-13P A.ai advertisement. Classify the quadrilaterals used in the logo. See Example 2 (p. 559) trapezoids and ograms 7. Algebra Find the value of x in the ogram at the right. See Example 3 (p. 560) Describe two different real-world items that are shaped like quadrilaterals. Then classify those quadrilaterals. Sample answer: chalkboard quadrilateral or rectangle; floor tile square 560 Chapter 10 Geometry: Angles and Polygons

4 PRACTICE EXTRA See page 684. Algebra Find the value of x in each quadrilateral. See Examples 1, 3 (pp. 558, 560) Classify each quadrilateral. See Example 2 (p. 559) 15. rectangle 16. square trapezoid 19. ogram quadrilateral 21. Many aircraft display the shape of the American flag slightly distorted to indicate motion. Classify each quadrilateral. See Example 2 (p. 559) The first figure is a rectangle. The second figure is a ogram Classify each quadrilateral. See Example 2 (p. 559) The first figure is a rectangle. The second figure is a trapezoid. Measure the angles and sides of each quadrilateral. Then use this information to classify each quadrilateral. 100 ; 90 ; 23. all 90 ; ; 60 ; ; 95 ; 2.3 cm, 120 ; 120 ; 2.1 cm, 1.3 cm, all 1.7 cm; 2.5 cm, 2.3 cm, 2.5 cm, 2 cm; 1.3 cm; quadrilateral rectangle Lesson 10-7 Quadrilaterals 561

5 26. Grace sorted a set of quadrilaterals into two categories according to a certain rule. The shapes that followed the rule were put in Set A, and the shapes that did not follow the rule were put in Set B. Set A square Set B rectangle ogram trapezoid What rule did Grace use to sort the quadrilaterals? Sample answer: The shapes have all sides. 27. Use the Internet or another source to look up the meaning of the term isosceles trapezoid. Explain how an isosceles trapezoid is related to an isosceles triangle. Then draw an example of an isosceles trapezoid. See margin. 28. OPEN ENDED Draw a rectangle using a ruler and protractor. Label each side and angle with its measure. Label all and perpendicular lines. See margin. 29. NUMBER SENSE Three of the angle measures of a quadrilateral are. Without calculating, determine if the measure of the fourth angle in each of the following situations is greater than, less than, or equal to 90. Explain your reasoning. See margin. a. The three angles each measure 89. b. The three angles each measure 90. c. The three angles each measure 91. CHALLENGE Determine whether each statement is sometimes, always, or never true. Explain your reasoning See margin. 30. A is a square. 31. A quadrilateral is a ogram. 32. A rectangle is a square. 33. A square is a rectangle. 34. SELECT A TOOL Quentin is designing a logo for his lawn care company. He wants to use polygons in the logo. Which of the following tools might Quentin use to design several sample logos? Justify your selection(s). Use the tool(s) to create a sample logo using polygons. Then classify each polygon you used in the sample logo. See margin. real objects paper/pencil technology 562 Chapter 10 Geometry: Angles and Polygons

6 35. Make a diagram that shows the relationship between each of the following shapes: rectangle, ogram, square,, quadrilateral, and trapezoid. Then write a few sentences that explain your diagram. See margin. 36 The drawing below shows the shape of Hinto s patio. B Hinto s Patio A A ogram is shown below. Find the measure of M to the nearest degree. H Find the measure of A. A 75 B 105 C 165 D 195 F 30 H 120 G 60 J 150 Algebra Find the value of x in each triangle. (Lesson 10-6) Tamika is working on a group project with 3 other students. They must decide who will be the researcher, the artist, the writer, and the presenter. How many ways can they choose to assign the jobs? (Lesson 10-5) 24 ways 42. Geometry Determine if the pair of lines marked on the polygon is best described as, perpendicular, or neither. (Lesson 10-4) 43. Mallory needs 4 _ 3 4 cups of flour for a _ bread recipe. Write 4 _ 3 4 as an improper fraction. (Lesson 4-4) 19 4 Self-Check Quiz at ca.gr5math.com Lesson 10-7 Quadrilaterals 563

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