Chapter 5 – Plane Geometry
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Chapter 5 – Plane Geometry 5-1 Points, Lines, Planes, and Angles 5-2 Parallel and Perpendicular Lines 5-3 Triangles 5-4 Polygons 5-5 Coordinate Geometry 5-6 Congruence 5-7 Transformations 5-8 Symmetry 5-9 Tessellations 5-1 Points, Lines, Planes & Angles Vocabulary Point – Names a location Line – Perfectly straight and extends in both directions forever Plane - Perfectly flat surface that extends forever in all directions Segment – Part of a line between two points Ray – Part of a line that starts at a point and extends forever in one direction Point Line Segment Ray Example 1 • • • • • Name four points Name the line Name the plane Name four segments Name five rays More Vocabulary Right Angle – Measures exactly 90° Acute Angle – Measures less than 90 ° Obtuse Angle – Measures more than 90 ° Complementary Angle – Angles that measure 90 ° together Supplementary Angle – Angles that measure 180 ° together Right Angle Acute Angle Obtuse Angle Complementary Angle Supplementary Angle Example 2 • • • • • Name the following: Right Angle Acute Angle Obtuse Angle Complementary Angle • Supplementary Angle Even MORE Vocabulary Congruent – Figures that have the same size AND shape Vertical Angles Angles A & C are VA Angles B & D are VA If Angle A is 60° what is the measure of angle B? Homework/Classwork Page 225, #13-34 5-2 Parallel and Perpendicular Lines Vocabulary Parallel Lines – Two lines in a plane that never meet, ex. Railroad Tracks Perpendicular Lines – Lines that intersect to form Right Angles Transversal – A line that intersects two or more lines at an angle other than a Right Angle Parallel Lines Perpendicular Lines Transversal Transversals to parallel lines have interesting properties The color coded numbers are congruent Properties of Transversals to Parallel Lines If two parallel lines are intersected by a transversal: The acute angles formed are all congruent The obtuse angles are all congruent And any acute angle is supplementary to any obtuse angle If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Symbols Parallel Perpendicular Congruent Example 1 In the figure Line X Y Find each angle measure In the figure Line A B Find each angle measure Homework/Classwork Page 230, # 6-20 5-3 Triangles Triangle Sum Theorem – The angle measures of a triangle in a plane add to 180° Because of alternate interior angles, the following is true: m1 m2 m 180 m1 m4 m3 m5 Vocabulary Acute Triangle – All angles are less than 90° Right Triangle – Has one 90° angle Obtuse Triangle – Has one obtuse angle Example Find the missing angle Example Find the missing angle. Example Find the missing angles Vocabulary Equilateral Triangle – 3 congruent sides and angles Isosceles Triangle – 2 congruent sides and angles Scalene Triangle – No congruent sides or angles Equilateral Triangle Isosceles Triangle Scalene Triangle Remember…they are ALL triangles Example Find the missing angle(s) Example Find the missing angle(s) Example Find the missing angle(s) Example Find the angles. Hint, remember the triangle sum theorem Classwork/Homework Page 237, #10-26 5-4 Polygons Polygons Have 3 or more sides Named by the number of sides “Regular Polygon” means that all the sides are equal length Polygon Triangle # of Sides 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 n-gon n Finding the sum of angles in a polygon Step 1: Divide the polygon into triangles with common vertex Step 2: Multiply the number of triangles by 180 The Short Cut 180°(n – 2) where n = the number of angles in the figure In this case n = 6 = 180°(6 – 2) = 180°(4) = 720° *Notice that n - 2 = 4 **Also notice that the figure can be broken into 4 triangles…coincidence? I don’t think so! Example Find the missing angle This chart may help… Polygon Total Angle measure Triangle # of Sides 3 Quadrilateral 4 360° Pentagon 5 540° Hexagon 6 720° Heptagon 7 900° Octagon 8 1080° n-gon n n° 180° Classwork/Homework Page 242, # 13-24
