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CHAPTER 8 Family Letter Section A What We Are Learning Dear Family, Lines and Angles In this section, your child will be learning the necessary terminology for understanding and applying the concepts of geometry. When given a figure, your child will be able to identify points, segments, rays, lines, and planes. Use the chart to review of these basic concepts. Vocabulary These are the math words we are learning: acute angle an angle that measures less than 90° adjacent angles angles with a common endpoint and side, but no common interior points Concept Definition Point An exact location in space. Line line a set of points that extends without end in opposite directions A Ray A Line Segment A Plane AB B A set of points that forms a flat surface that extends forever. A C plane ABC B Your child will also learn that congruent figures are figures that have the same shape and the same size. Congruent line segments are segments that are the same length. Congruent sides and segments are marked with an equal number of tick marks. Identify the line segments that are congruent. plane a set of points that forms a perfectly flat surface that extends forever A WZ BC AC YZ W one tick mark two tick marks Y B Copyright © by Holt, Rinehart and Winston. All rights reserved. AB B A part of a line with two endpoints. obtuse angle an angle whose measure is greater than 90° but less than 180° perpendicular lines lines that intersect to form right angles B Part of a line that has one endpoint and extends forever. line segment a part of a line with two endpoints parallel lines lines that are in the same plane and never intersect AB A set of points that extends without end in opposite directions. congruent having the same size and shape congruent angles angles that have the same measure point P P angle two rays with a common endpoint complementary angles two angles whose measures add to 90° Symbols C Z 61 Holt Mathematics CHAPTER 8 Family Letter Section A, continued point an exact location in a plane ray a part of a line that has one endpoint and extends forever Another geometric concept your child will be learning involves angles and angle relationships. Your child will recognize and classify angles into four different categories: acute, obtuse, right, and straight. right angle an angle that measures exactly 90° skew lines lines that lie in different planes. They are neither intersecting nor parallel straight angle an angle that measures exactly 180° supplementary angles two angles whose measures have a sum of 180° Acute 90° Obtuse 90° Right 90° Straight 180° Lines also have special relationships. Intersecting lines that form right angles are called perpendicular lines. Lines that are in the same plane, but do not cross, are called parallel lines. If two parallel lines are cut by a third line, or a transversal, all of the acute angles are congruent and all of the obtuse angles are congruent. Lines that are not in the same plane and never intersect are called skew lines. transversal a line that intersects two or more lines vertex the common endpoint formed by two rays vertical angles a pair of opposite congruent angles formed by intersecting lines Perpendicular Lines Parallel Lines Parallel Lines cut by a transversal The information covered in this section will provide a strong foundation for the geometric concepts and applications your child will be using throughout this chapter and future mathematics courses. Sincerely, Copyright © by Holt, Rinehart and Winston. All rights reserved. 62 Holt Mathematics Name CHAPTER 8 Date Class Family Letter Lines and Angles Use geometry notation to identify the figures. D F C A E 1. points B 2. lines 3. rays Tell whether each angle is acute, right, obtuse, or straight. 4. 5. 6. Use the figure to the right for Exercises 7–11. 7. Name one pair of complementary angles. E B 8. Name two pairs of supplementary angles. P 50° 90° G H 140° D Tell the measure of each angle. 9. PGB 10. DGH 11. EGH Find the measures of 1 and 3. 12. m1 13. m3 135° 1 3 3. Possible answer: AF , AD , AE , AB , FB Answers: 1. A, B, C, D, E, F 2. Possible answer: ED 4. straight 5. obtuse 6. acute 7. BGP and PGD 8. DGB and BGE, EGH and HGD 9. 50° 10. 140° 11. 40° 12. 45° 13. 45° Copyright © by Holt, Rinehart and Winston. All rights reserved. 63 Holt Mathematics Name CHAPTER 8 Date Class Family Fun Geometric Baseball Materials 1 number cube Vocabulary words from this chapter Marker pieces Directions • Split into two teams. • The person “batting” tells what you “hit”. 1 – a single 2 – a double 3 – a triple rolls the number cube. The number on the cube 4 – a home run 5 – strike 6 – out • In order to get on base, you must correctly define a geometry term. If you do not define the word correctly, it is an out. The more words your team correctly defines, the better chance you have to move your team around the bases. The words may come from anywhere in this chapter. • After 3 outs, the teams switch places. • The team with the most runs after 5 innings wins the game. Scoreboard Team 1 Team 2 2 3 1 H Copyright © by Holt, Rinehart and Winston. All rights reserved. 64 Holt Mathematics