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## 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**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**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**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**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**Triangle Sum Theorem – The angle measures of a triangle in**a plane add to 180° Because of alternate interior angles, the following is true: 5-3 Triangles**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**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**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!