Geometry: 1-1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the two ways? Give an example of each: What is a Plane? There are two ways to name a line. What are the two ways? Give an example of each. Define Collinear: Define Noncollinear: 1
Define intersection: Exercises 1. Draw and Label a point, line and plane. Refer to the figure. 2. Name the intersection of plane N and line AE. 3. Name the intersection of BC and DC. 4. Does DC intersect AE? Explain. Refer to the figure. 5. Name the three line segments that intersect at point A. 6. Name the line of intersection of planes GAB and FEH. 7. Do planes GFE and HBC intersect? Explain. 8. Are G, D and B coplanar? 9. Are F, H, and A coplanar? 10. Are F, H and B coplanar? 2
Describe what you see in as many ways as you can. 1. 2. 3. Plane N contains line b. 4. Planes R and S intersect at line MN. 5. A, B, and C do not intersect. 3
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Geometry: 1-2 Linear Measure What is the difference between a line and a line segment? Define congruent: What is the congruent symbol? How are congruent segments labeled in a figure? Segment Addition Postulate Exercises 1. Find the value of x and KL if K is between J and L. JK = 2x, KL = x + 2, and JL = 5x 10 2. Find the value of x and YZ if Y is between X and Z. XY = 2x + 1, YZ = 6x, and XZ = 81 5
3. Find the value of x and JL if K is between J and L. JK=x 2 21x, KL= 2x, and JL= 60. 4. Point B is between A and C. If AB= x 2 + 2x, AC= 13x - 2 and BC= 46. Find the value of x. 6
Geometry: 1-3 Distance and Midpoint Use the number line to find the distance of AB Use the coordinate plane to find the distance of KL K (-2, 10), L(-4, 3) There are two ways. 1. Make a right triangle 2. Use the distance formula Without a coordinate plane find the distance of EF E(-12, 2), F(-9, 6) Define Midpoint: 7
Use the number line to find the coordinate of the midpoint of each segment. CE Find the coordinates of the midpoint of EF where E (-2, 6), F (-9, 3) Find the coordinates of the missing endpoint if E is the midpoint of DF where D(-3, -8), E(1, -2) 8
Geometry: 1-4 (day 1) Angle Measure Use your book to complete the following Define Ray: How is a ray named? Give an example Define Opposite Ray: Draw a picture of opposite rays and name the two rays. Define angle: Draw an angle and then identify it s parts. Angles are measure in units called Name the ways to classify the angles, define them and draw a picture. Exercises Refer to the figure at the right. 1. Name the vertex of 4. 2. Name the sides of BDC. 3. Write another name for DBC. 9
Geometry: 1-4 (day 2) Angle Measure Complete the sketch in geometer s sketchpad. Angle Addition Postulate Sketch 1. Draw an angle 2. Measure each angle my selecting the three points in order that you would say them if you were naming it. Go to measure, angle. Drag the measurement by the angle. 3. Draw a ray that is on the interior of the angle by using the line segment tool. 4. Measure the two angles that are created. Remember to select the points in order that you would use when naming it. Place the measurement by the angles. 5. Add the two smaller angles together by going to measure, calculate. Click on one of the measures, click the add symbol on the calculator, click on the other measure. Click okay. 6. What do you notice about the sum of those two measures compared to the original? Angle Bisector Sketch- Start a new sketch 1. Draw an angle 2. Measure each angle my selecting the three points in order that you would say them if you were naming it. Go to measure, angle. Drag the measurement by the angle. 3. Create an angle bisector by selecting the point in order that you would name the angle, go to construct, angle bisector. 4. Measure the two angles that are created. Remember to select the points in order that you would use when naming it. Place the measurement by the angles. 5. What do you notice? 6. What does it mean to bisect an angle? 10
Angle Addition Postulate: Angle Bisector: Congruent angles: 11
Exercises 1. In the figure BA and BC are opposite rays. BF bisects CBE. If m EBF = 6x + 4 and m CBF = 7x - 2, find m EBF. 2. In the figure BA and BC are opposite rays. BF bisects CBE. Let m 1 = m 2. If m ABE = 100 and m ABD = 2(r + 5), find r and m DBE 12
Geometry: 1-5 (day 1) Angle Relationship Complete the following Chart using your book Special Angle Pairs Adjacent Angles Definition Example Nonexample Linear Pair Definition Example Nonexample Vertical Angles Definition Example Nonexample Define Complementary angles and draw examples Define Supplementary angles and draw 2 different examples 13
What is the difference between linear pair angles and supplementary angles? Define Perpendicular lines What is the symbol that represents perpendicular? Draw two lines that are perpendicular. What would you do to the picture to communicate to others that the lines are perpendicular? Excercises Name an angle or angle pair that satisfies each condition. 1. two adjacent angles 2. two acute vertical angles 3. two supplementary adjacent angles 4. an angle supplementary to RTS For Exercises 5 7, use the figure at the right. 5. Identify two obtuse vertical angles. 6. Identify two acute adjacent angles. 7. Identify an angle supplementary to TNU. 14
Geometry: 1-5 (day 2) Angle Relationship Vertical angle are two nonadjacent angles that are formed by two intersecting lines. Complete the sketch in geometer s sketchpad Vertical angles sketch: 1. Using the line segment tool draw two line segments that intersect. 2. Measure all four angles. Remember to click on the point in the order that you would name the angle. This is not necessarily alphabetically. Move the measurements to the angle that they represent. 3. Look at the vertical angles. What do you notice about vertical angles? 4. Using the calculator in sketchpad add two angle that are next to each other. (if you don t remember see sketch from 1-4 angle addition postulate sketch step 5) Exercises 1. Find the value of y, m RPT, and m TPW 2. Find the value of x and m CBA 15
3. Find the value of x, then determine if AB CD 16
Geometry: 1-6 Two-Dimensional Figures Define Polygon. Draw one and label the parts. What is the difference between a concaved polygon and a convex polygon? Polygons can be classified by the sides. Complete the chart Number of sides Polygon Name 3 9 4 10 5 11 6 12 7 13 8 14 9 Define Equilateral Polygon and draw one. Number of sides Polygon Name Define Regular Polygon and draw one. A regular polygon with 3 sides is called A regular polygon with four sides is called. 17
Exercises Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Find the perimeter and area of the following. Graph the following then find the perimeter and area. 18
Geometry: 1-7 Three-Dimensional Figures Using your book complete the following: Define Polyhedron What is a face of a polyhedron? What is an edge of a polyhedron? Write the name of each shape below it and determine if it is a polyhedron Exercises Determine whether each solid is a polyhedron and complete the following 1 2. Polyhedron? Polyhedron? Faces? Faces? Edges? Vertices? Edges? Vertices? 19
Surface area and Volume Prism: Surface area Volume Formula: Formula: Pyramid Surface area Volume Formula: Formula: Cylinder Surface area Volume Formula: Formula: 20