Plane Geometry Points Lines Planes Angles Vocabulary p
Plane Geometry
Points, Lines, Planes & Angles Vocabulary p Point – Names a location p Line – Perfectly straight and extends in both directions forever p Plane - Perfectly flat surface that extends forever in all directions p Segment – Part of a line between two points p 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° p Acute Angle – Measures less than 90 ° p Obtuse Angle – Measures more than 90 ° p Complementary Angle – Angles that measure 90 ° together p Supplementary Angle – Angles that measure 180 ° together p
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 p Congruent – Figures that have the same size AND shape p Vertical Angles n n p Angles A & C are VA Angles B & D are VA If Angle A is 60° what is the measure of angle B?
Parallel and Perpendicular Lines Vocabulary p Parallel Lines – Two lines in a plane that never meet, ex. Railroad Tracks p Perpendicular Lines – Lines that intersect to form Right Angles p Transversal – A line that intersects two or more lines at an angle other than a Right Angle
Parallel Lines
Perpendicular Lines
Transversal
p Transversals to parallel lines have interesting properties p The color coded numbers are congruent
Properties of Transversals to Parallel Lines p If two parallel lines are intersected by a transversal: n n n p 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 p Parallel p Perpendicular p Congruent
Example 1 p In the figure Line X Y p Find each angle measure
p In the figure Line A B p Find each angle measure
Triangles p Triangle Sum Theorem – The angle measures of a triangle in a plane add to 180° n Because of alternate interior angles, the following is true:
Vocabulary p Acute Triangle – All angles are less than 90° p Right Triangle – Has one 90° angle p Obtuse Triangle – Has one obtuse angle
Example p Find the missing angle
Example p Find the missing angle.
Example p Find the missing angles
Vocabulary p Equilateral Triangle – 3 congruent sides and angles p Isosceles Triangle – 2 congruent sides and angles p Scalene Triangle – No congruent sides or angles
p Equilateral Triangle p Isosceles Triangle p Scalene Triangle
Remember…they are ALL triangles
Example p Find the missing angle(s)
Example p Find the missing angle(s)
Example p Find the missing angle(s)
Example p Find the angles. Hint, remember the triangle sum theorem
Polygons p Polygons n n n Have 3 or more sides Named by the number of sides “Regular Polygon” means that all the sides are equal length Polygon # of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 n-gon n
Finding the sum of angles in a polygon p Step 1: n Divide the polygon into triangles with common vertex
p Step 2: n Multiply the number of triangles by 180
The Short Cut 180°(n – 2) where n = the number of angles in the figure p In this case n = 6 p = 180°(6 – 2) p = 180°(4) p = 720° p *Notice that n - 2 = 4 **Also notice that the figure can be broken into 4 triangles…coincidence? I don’t think so!
Example p 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°
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