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Introduction to Geometry: Points, Lines, and Planes PRE-ALGEBRA LESSON 9-1 Quick Check Use the figure to name each of the following. a. four points H, I, J, and K Name a point with a capital letter. b. four different segments HO, HJ , KI, and OI Name a segment by its endpoints. c. five other names for KI IK , KO, OK , IO , and OI Horizontal line KI has several names. d. five different rays HO, OJ, KI , OK , and JH The first letter names the endpoint. 9-1 Introduction to Geometry: Points, Lines, and Planes PRE-ALGEBRA LESSON 9-1 You are looking directly down into a wooden crate. Name each of the following. a. four segments that intersect PT MP, OP, QT, ST b. three segments parallel to PT MQ, NR, OS c. four segments skew to PT MN, NO, QR, RS Quick Check 9-1 Introduction to Geometry: Points, Lines, and Planes PRE-ALGEBRA LESSON 9-1 Draw two intersecting lines. Then draw a segment that is parallel to one of the intersecting lines. Use the lines on notebook or graph paper. First draw two lines that intersect. Then draw a segment that is parallel to one of the lines. Quick Check 9-1 Introduction to Geometry: Points, Lines, and Planes PRE-ALGEBRA LESSON 9-1 Use the figure. Name each of the following. 1. four points A, B, C, D 2. another name for EA 3. three different rays EQ AQ, AE, GR 4. three segments that are parallel to HG 5. four segments that are skew to CG 6. four segments that intersect AE 9-1 EF, DC, AB AB, AD, EF, EH AB, AD, EF, EH Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 The Jackson County Bird Sanctuary has three times as many owls as hawks. It has 40 hawks and owls in all. How many of each are in the sanctuary? 30 owls, 10 hawks 9-2 Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 (For help, go to Lesson 7-5.) Solve. 1. n + 45 = 180 2. 75 + x = 90 3. 3y = 2y + 90 4. 2a + 15 = a + 45 Check Skills You’ll Need 9-2 Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 Solutions 1. n + 45 = 180 n + 45 – 45 = 180 – 45 n = 135 2. 75 + x = 90 75 – 75 + x = 90 – 75 x = 15 3. 3y = 2y + 90 3y – 2y = 2y – 2y + 90 y = 90 4. 2a + 15 = a + 45 2a – a + 15 = a – a + 45 a + 15 = 45 a + 15 – 15 = 45 – 15 a = 30 9-2 Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 Find the measure of m m m 3+m 3 if m 4 = 180° 4 = 110°. 3 and 4 are supplementary. 3 + 110° = 180° Replace m 4 with 110°. 3 + 110° – 110° = 180° – 110° Solve for m 3. m 3 = 70° Quick Check 9-2 Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 In the diagram, p || q. Identify each of the following. a. congruent corresponding angles 1 3, 2 4, 5 7, 6 8 b. congruent alternate interior angles 2 7, 6 3 Quick Check 9-2 Angle Relationships and Parallel Lines PRE-ALGEBRA LESSON 9-2 In the diagram, d e. 1. Find the m 5 if m 8 is 35°. 145° 2. Name the congruent corresponding angles. 1 5, 2 6, 4 8, 3 7 3. Name the congruent alternate interior angles. 4 7, 2 5 9-2