Objectives: (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes
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1 Geometry Chapter 1 Outline: Points, Lines, Planes, & Angles A. 1-1 Points, Lines, and Planes (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes DEFINE (left brain) the following terms: SKETCH (right brain): 1. Point: 2. Line: 3. Collinear: Non-collinear: 4. Plane: 5. Coplanar: Non-coplanar Example 1: AL GEO Algebra Connection: Ordered Pairs- Two numbers (x, y) given in a specific order used to locate a point on a coordinate gird. Draw and label this relationship: plane R contains lines (AB) and (DE), which intersect at P. Add point c on plane R so that it is not collinear with (AB) or (CD) Define: Space- Since it is impossible to show, or draw, an entire plane, planes will be represented by shaded areas (usually using color), and dashed lines will be used to represent the edges of the three-dimensional figure that we cannot see. Assignment: page 9-11: all, all, 54, 56, 58, 59 Define: locus
2 B. 1-2 Linear Measure and Precision Objective: Can you read the measurements on a ruler? A protractor? DEFINE (left brain): SKETCH (right brain): Example 3: Recall that for any two real numbers a and b, there is a real number n between a and b such that a< n < b. This relationship also applies to points on a line and is called. Point M is between points P and Q iff P, Q, and M are and. Example 4: Symbol: Line segment- Precision- Congruent- Assignment: page 17-18: (in class), 16, 18, 21, even, 46, 47, 50 C. 1-3 Distance and Midpoints Can you find the distance between two points without a ruler?
3 Formulas: DISTANCE between two points on a NUMBER LINE: DISTANCE between two points on a COORDINATE PLANE: Midpoint MIDPOINT between two points on a NUMBER LINE: MIDPOINT between two points on a COORDINATE PLANE: You can also find the coordinates of the endpoint of a segment if you know the coordinates of the other endpoint and the midpoint. Example 5: Algebra Connection: Segment Bisector-
4 Assignment: Page 25-27: even 48 (in class) 49 a,c 50-53, 55 D. 1-4 Angle Measure Who was Claudius Ptolemy? Ray- Opposite Rays- Angle- Sides- Vertex- An angle is formed by two. Symbols-reading angles: It is very important that you know how to read and write angles in geometry! An angle is divided into three distinct parts: Measuring angles with a protractor: Draw any angle and measure it. Draw a 70 degree angle exactly. Angles can be classified by their measures: Right Acute Obtuse
5 What is a straight angle? Congruent Angles are angles that. MODEL: Algebra Example 3: Angle Bisector- Assignment: Pg : even, 43, 44, 45-48, 50 E. 1-5 Angle Relationships Identify and use special angle pairs Identify perpendicular lines *Remember these angle relationships because they will be used through out the textbook! Adjacent Angles- Vertical Angles- Linear Pair- Example1: Complementary (or complimentary?) Angles- Supplementary Angles- * While the other angle pairs in this lesson share at least one point, complementary and supplementary angles need not share any points!
6 Algebra Connection: 1. Find the measure of two complementary angles if the difference in the measure of the two angles is Find the m if m is 20 more than four times its supplement. Perpendicular Lines- symbol: ( ) Perpendicular lines intersect to. Perpendicular lines intersect to. Segments and rays can be. The right angle symbol. *In geometry figures are used to depict a situation; do not assume certain relationships exist unless told so. p.40 Assignment: pg : all, 18, 20, 22, all 31-35, 37 F. 1-6 Polygons Polygon- Concave Polygons: Convex Polygons: Regular Polygons:
7 Table: # of sides Polygon 3 Triangle n Perimeterformulas: Triangle Square Rectangle Find the length of each side of the polygon for the given perimeter: (p.50) P = 41 yards Example3: Coordinate Geometry. Find the perimeter of triangle PQR. P( -5, 1 ) Q( -1, 4), R( -6, -8) To solve this problem use the formula! Assignment: Pg : 12-14, 19-23, 28, 29-34, 36 Chapter Test Date:
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