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1 Date Name of Lesson Assignments & Due Dates Basic Terms Points, Lines and Planes Constructions (Copy Angle and Segment) Distance Formula Activity for Distance Formula Midpoint Formula Quiz Angle Measure Angle Relationships Angle Bisectors (Construct and Measurements of Angle Bisector) Review & Quiz Practice Test Practice Test & Card Review Unit Test 1
2 Basic Terms Notes Term Geometric Figure Additional Information Supplementary Angles Two angles with measures that have a sum of 180. Complementary Angles Vertical Angles Adjacent Angles Congruence Two angles with measures that have a sum of 90. Two nonadjacent angles formed by two intersecting lines. Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points. Having the same measure. Similarity Transformations Having the same shape but possibly different sizes. In a plane, mapping each point of a pre-image to an image. Reflection Rotation Translation Parallel Lines A transformation representing a flip of the figure over a point, line, or plane. A transformation that turns every point of a pre-image through a specified angle direction about a fixed point, called the center of rotation. A transformation that moves all points of a figure the same distance in the same direction. Coplanar lines that do not intersect. Perpendicular Lines Lines that form right angles. Transversal A line that intersects two or more lines in a plane at different points. 2
3 Term Geometric Figure Ways to Reference the Figure Point A point is a location. In a figure, points are represented by a dot. Line A line is made up of points and has no thickness or width. Plane Line Segment Ray A plane is a flat surface made up of points that has no depth and extends indefinitely in all directions. A measureable part of a line that consists of two points, called endpoints, and all the points between them. Contains an endpoint and all the points in a line in one direction. Collinear Points Points that lie on the same line. Coplanar Points Points that lie in the same plane. Linear Pair Midpoint Between-ness of points A pair of adjacent angles whose non-common sides are opposite rays. The point on a segment exactly halfway between the endpoints of the segment. For any points A and B on a line, there is another point C between A and B if and only if A, B, and C are collinear and AC + CB = AB. 3
4 Points, Lines, and Planes Notes Use the figure to name each of the following. 1. a line containing the point W 2. a plane containing the point X 3. a plane containing the points T and Z 4. a line containing the point T Draw and label a figure for each relationship. 5. Lines AB and CD intersect at E for A(-2, 4), B(0, -2), C(-3, 0), and D(3, 3) on a coordinate plane. Point F is coplanar with these points but not collinear with AB or CD. 6. QR intersects plane T at point S. 7. How many planes appear in the figure? 8. Name three points that are collinear. 9. Name the intersection of planes HDG with plane X. 10. At what point do LM and EF intersect? Explain. 4
5 Constructions Notes Steps for Constructing a Copy of a Line Segment 1. Start with a line segment PQ that we will copy. 2. Mark a point R that will be one endpoint of the new line segment. 3. Set the compasses' point on the point P of the line segment to be copied. 4. Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ. 5. Without changing the compasses' width, place the compasses' point on the point R on the line you drew in step Without changing the compasses' width, draw an arc roughly where the other endpoint will be. 7. Pick a point S on the arc that will be the other endpoint of the new line segment. 8. Draw a line from R to S. The line segment RS is equal in length (congruent to) the line segment PQ
6 Steps for Constructing a Copy of an Angle 1. Start with an angle BAC that we will copy. 2. Make a point P that will be the vertex of the new angle. 3. From P, draw a ray PQ. This will become one side of the new angle. o This ray can go off in any direction. o It does not have to be parallel to anything else. o It does not have to be the same length as AC or AB. 4. Place the compasses on point A, set to any convenient width. 5. Draw an arc across both sides of the angle, creating the points J and K. 6. Without changing the compasses' width, place the compasses' point on P and draw a similar arc there, creating point M. 7. Set the compasses on K and adjust its width to point J. 8. Without changing the compasses' width, move the compasses to M and draw an arc across the first one, creating point L where they cross. 9. Draw a ray PR from P through L and onwards a little further. The exact length is not important. The angle RPQ is congruent (equal in measure) to angle BAC
7 Distance Formula Notes Distance Distance Formula on a Number Line Use the number line to find the distance between the two points. 1. BE 2. CF 3. AF 4. DF Distance Formula (in Coordinate Plane) 5. Find the distance between C( 4, 6) and D(5, 1). 6. Find the distance between J(4, 3) and K( 3, 7). 7
8 Midpoint Formula Notes Midpoint Midpoint Formula (on Number Line) 1. Jessica hangs a picture 15 inches from the left side of a wall. How far from the edge of the wall should she mark the location for the nail the picture will hang on if the right edge is 37.5 inches from the wall s left side? Midpoint Formula (in Coordinate Plane) 2. Find the coordinates of M, the midpoint of ST for S( 6, 3) and T(1, 0). 3. Find the coordinates of M, the midpoint of GH, for G(8, 6) and H( 14, 12). 4. Find the coordinates of J if K( 1, 2) is the midpoint of JL and L has the coordinates (3, 5). 5. Find the coordinates of D if E( 6, 4) is the midpoint of DF and F has the coordinates ( 5, 3) 8
9 Ray Angle Measure Notes Opposite Rays Angle Sides Vertex Naming an Angle Points on a Plane with an Angle Use the map of a high school shown to answer the following. 1. Name all angles that have B as a vertex. 2. Name the sides of What is another name for GHL? 4. Name a point in the interior of DBK. 9
10 5. Name all angles that have B as a vertex. 6. Name the sides of Write another name for 6. Degree Classify Angles right angle acute angle obtuse angle 10
11 Classify each angle as right, acute, or obtuse. Then use a protractor to measure the angle to the nearest degree. 8. MJP 9. LJP 10. NJP 11. TYV 12. WYT 13. TYU 11
12 Angle Relationships Notes Special Angles Pairs Name and Definition Examples Nonexamples Adjacent Angles Linear Pair Vertical Angles Name an angle pair that satisfies each condition. 1. two acute adjacent angles 2. two obtuse vertical angles 3. two angles that form a linear pair 4. two acute vertical angles 12
13 Angle Pair Relationships Vertical Angles Complementary Angles Supplementary Angles Linear Pair 5. Find the measures of two supplementary angles if the measures of one angles is 6 less than five times the measure of the other angle. 6. Find the measures of two supplementary angles if the difference in the measures of the two angles is
14 Perpendicular Lines 7. Find x and y so that PR and SQ are perpendicular. 8. Find x and y so that KO and HM are perpendicular. 14
15 CAN be Assumed Interpreting Diagrams CANNOT be Assumed Determine whether each statement can be assumed from the figure. Explain. 9. KHJ and GHM are complementary 10. GHK and JHK are a linear pair 11. HL is perpendicular to HM 12. m VYT = TYW and TYU are supplementary 14. VYW and TYS are adjacent angles 15
16 Angle Bisector Angle Bisectors Notes 1. In the figure, KJ and KM are opposite rays, and KN bisects JKL. If m JKN = 8x 13 and m NKL = 6x + 11, find m JKN. 2. In the figure, BA and BC are opposite rays, and BH bisects EBC. If m ABE = 2n + 7 and m EBF = 4n 13, find m ABE. 16
17 Steps to Bisecting an Angle 1. Start with angle PQR that we will bisect. 2. Place the compasses' point on the angle's vertex Q. 3. Adjust the compasses to a medium wide setting. The exact width is not important. 4. Without changing the compasses' width, draw an arc across each leg of the angle. 5. The compasses' width can be changed here if desired. Recommended: leave it the same. 6. Place the compasses on the point where one arc crosses a leg and draw an arc in the interior of the angle. 7. Without changing the compasses setting repeat for the other leg so that the two arcs cross. 8. Using a straightedge or ruler, draw a line from the vertex to the point where the arcs cross. This is the bisector of the angle PQR. Construct an angle bisector
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