Section 9.1. Points, Lines, Planes, and Angles. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
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1 Section 9.1 Points, Lines, Planes, and Angles
2 INB Table of Contents Date Topic Page # May 19, 2014 Test #1 Practice Test 14 May 19, 2014 Test #1 Practice Test Workspace 15 May 19, 2014 Section 9.1 Examples/Foldable 16 May 19, 2014 Section 9.1 Notes 17 May 19, 2014 Section 9.2 Examples 18 May 19, 2014 Section 9.2 Notes
3 What You Will Learn Points Lines Planes Angles 9.1-3
4 Basic Terms Description Diagram Symbol Line AB A B AB Ray AB A B AB Ray BA A B BA Line segment AB A B AB 9.1-4
5 Plane We can think of a plane as a twodimensional surface that extends infinitely in both directions. Any three points that are not on the same line (noncollinear points) determine a unique plane
6 Plane Two lines in the same plane that do not intersect are called parallel lines
7 Angles An angle is the union of two rays with a common endpoint; denoted
8 Angles The vertex is the point common to both rays. The sides are the rays that make the angle. There are several ways to name an angle: ABC, CBA, B 9.1-8
9 Angles 9.1-9
10 Types of Angles Adjacent Angles - angles that have a common vertex and a common side but no common interior points. Complementary Angles - two angles whose sum of their measures is 90 degrees. Supplementary Angles - two angles whose sum of their measures is 180 degrees
11 Example 3: Determining Complementary Angles In the figure, we see that ABC = 28 ABC & CBD are complementary angles. Determine m CBD
12 Example 3: Determining Supplementary Angles In the figure, we see that ABC = 28. ABC & CBE are supplementary angles. Determine m CBE
13 Definitions When two straight lines intersect, the nonadjacent angles formed are called Vertical angles. Vertical angles have the same measure
14 Special Names Alternate interior angles 3 & 6; 4 & 5 Alternate exterior angles 1 & 8; 2 & 7 Corresponding angles 1 & 5, 2 & 6, 3 & 7, 4 & 8 Interior angles on the opposite side of the transversal have the same measure Exterior angles on the opposite sides of the transversal have the same measure One interior and one exterior angle on the same side of the transversal have the same measure
15 Example 6: Determining Angle Measures The figure shows two parallel lines cut by a transversal. Determine the measure of 1 through
16 Section 9.2 Polygons
17 What You Will Learn Polygons Similar Figures Congruent Figures
18 Polygons A polygon is a closed figure in a plane determined by three or more straight line segments
19 Polygons Polygons are named according to their number of sides. Number of Sides Name Number of Sides Name 3 Triangle 8 Octagon 4 Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Hexagon 12 Dodecagon 7 Heptagon 20 Icosagon
20 Polygons Sides Triangles Sum of the Measures of the Interior Angles 3 1 1(180º) = 180º 4 2 2(180º) = 360º 5 3 3(180º) = 540º 6 4 4(180º) = 720º The sum of the measures of the interior angles of an n-sided polygon is (n 2)180º
21 Example 3: Using Similar Triangles to Find the Height of a Tree Monique Currie plans to remove a tree from her backyard. She needs to know the height of the tree. Monique is 6 ft tall and determines that when her shadow is 9 ft long, the shadow of the tree is 45 ft long (see Figure). How tall is the tree?
22 Example 3: Using Similar Triangles to Find the Height of a Tree
23 Example 3: Using Similar Triangles to Find the Height of a Tree
24 Congruent Figures If corresponding sides of two similar figures are the same length, the figures are congruent. Corresponding angles of congruent figures have the same measure
25 Quadrilaterals Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360º. Quadrilaterals may be classified according to their characteristics
26 Example 5: Angles of a Trapezoid Trapezoid ABCD is shown. a) Determine the measure of the interior angle, x. b) Determine the measure of the exterior angle, y
27 Example 5: Angles of a Trapezoid
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