Table of Contents Syllabus Unit 1 Fundamentals of Geometry Concept 1 Geometric Terms Homework Concept 2 Collinear and Coplanar Homework Concept 3 Intersections Homework Concept 4 Measuring Postulates ID: 1044283
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1. Honors Geometry Notebook
2. Table of ContentsSyllabusUnit 1: Fundamentals of GeometryConcept 1: Geometric TermsHomeworkConcept 2: Collinear and CoplanarHomeworkConcept 3: IntersectionsHomeworkConcept 4: Measuring Postulates HomeworkConcept 5: Bisector, Midpoint, and Distance FormulaHomeworkConcept 6: Angles and Angle Bisectors HomeworkConcept 7: Angle Pairs HomeworkReviewUnit 2: LogicConcept 8: Inductive ReasoningHomeworkConcept 9: Compound Statements/Truth TablesHomeworkConcept 10: Conditional StatementsHomeworkConcept 11: Biconditional StatementsHomeworkConcept 12: Deductive ReasoningHomeworkReviewUnit 3: Proofs, Angles and Parallel LinesConcept 13HomeworkConcept 14HomeworkConcept 15HomeworkConcept 16HomeworkConcept 17HomeworkConcept 18HomeworkReview
3. PointTable of ContentsConcept 1:Opposite RaysRayLinePlaneLine SegmentExamples
4. PointBackDefinition: Illustration: Naming: A specific location in space, usually represented with a dot. point A A
5. LineBackDefinition: Illustration: Naming: The set of all point or AB
6. PlaneBackDefinition: Illustration: Naming: A flat, two-dimensional surface that extends infinitely in both directions.plane G, plane ABC GACBplane ACB, plane BACplane BCA, plane CAB, or plane CBA
7. Line SegmentBackDefinition: Illustration: Naming: A portion of a line with two endpoints (a start and end point) and all the points between them.AB
8. RayBackDefinition: Illustration: Naming: A portion of a line with an initial point and a direction. (Keeps going in one direction.)Or ray AB AB
9. Opposite RaysBackDefinition: Illustration: Naming: Two rays with the same initial point and go in opposite directions to form a line.ABC
10. Table of ContentsExamples LineSegmentRayAnglesPlanePointHas exactly one point Has two endpoints Extends forever Can be measured Can be cut in half Labeled with one letter Labeled with 2 letters Labeled with 3 letters MoreXXXXXXXXXXXXXXXXXXX
11. Table of ContentsExamplesRefer to the figure.1. Name a line that contains point A. 2. What is another name for line m?3. Name a point not on 4. What is another name for line l?5. Name a point not on line l or line m. More
12. Table of ContentsExamples6. Name a line that contains points T and P.7. Name a line that is not contained in plane S.8. Name the plane that contains and Name the geometric term(s) modeled by each object.9. 10. 11.12. A car antenna 13. a library card
13. Table of ContentsConcept 2:Colinear and CoplanarCollinearNon-CollinearCoplanarNon-CoplanarExamples
14. Collinear Non-CollinearBackDefinition: Definition: Example: Example: Two or more points that lie on the same line.Points that do not lie on the same line.CollinearPoints E, R, BPoints F, R, BAny two points can be collinear. A line can be drawn through them.CollinearThey all lie on the same line
15. Coplanar Non-CoplanarBackDefinition: Definition: Example: Example: Points or lines that lie on the same planePoints or lines that do not lie on the same plane.CoplanarPoints Y, E, RPoints F, R, EA is on a different plane than points F and Y.Non-coplanarThey all lie on the same line so they are in the same plane.
16. Table of ContentsRefer to the figure.1. How many planes are shown in the figure?2. Name two points collinear to point S.3. Name two points coplanar to point T.4. Name a point that is non-coplanar with point R. 5. Are points N, R, S, and W coplanar? Explain.6 planesPoints X and MPoints Q, P and WPoint WNo because point W is in a different plane.
17. Table of ContentsDraw and label a figure for each relationship.6. is in plane Q. 8. Point Y is not collinear with points T and P. 7. Point X is collinear with points A and P. 9. Line ℓ contains points X and Y. QABTYPAPXℓXY
18. Table of ContentsConcept 3: Intersections Intersection of LINES and PLANESTwo line intersect at:A plane and a line intersect at: Two planes intersect at:Examples
19. Two LINES intersect at: ______________ A pointPoint MBack
20. BackTwo PLANES intersect at: ______________ A lineLine XZ
21. BackA PLANE and a LINE intersect at: ______________ A pointPoint G
22. Refer to the figure.1. Name the intersection of the planes O and N. 2. Does intersect point D? Explain.No, point D is on the plane with line AB, but not collinear.3. Name the intersection of plane N and . point B4. Name the intersection of and . point C5. Does intersect ? Explain. No, is in a different plane that and doesn’t run into it. 6. Name the three line segments that intersect at point A. 7. Name the line of intersection of planes GAB and FEH. 8. Do planes GFE and HBC intersect? Explain. Yes, they intersect at . Table of ContentsExamples
23. Table of ContentsConcept 4: Measuring Postulates Examples
24. BackRuler PostulateThe y-values are the same so find the difference in the x-values.AB = |4 - -1| = |5| = 5AB = |2 - -3| = |5| = 5CD = |5 - 1| = |4| = 4AB = |1- 6| = |-5| = 5CD = |8 - 3| = |5| = 5
25. BackAB + BC = AC AB + BC = AC AB + BC = AC
26. Length in Metric Units1. Find the length of AB using the ruler.The ruler is marked in millimeters.Answer: AB is about 42 millimeters long.
27. 2. Find the length of AB using the ruler.Each centimeter is divided into fourths.Answer: AB is about 4.5 centimeters long.
28. Length in Standard UnitsEach inch is divided into sixteenths. 3.
29. 4.Each inch is divided into forths.
30. Table of ContentsExamplesFind the measurement of each segment. Assume that each figure is not drawn to scale.MorePQ + QS = PS AC + CD = AD WX + XY = WY
31. Table of ContentsMore ExamplesALGEBRA Find the value of x and KL if K is between J and L.8. JK = 6x, KL = 3x, and JL = 27 9. JK = 2x, KL = x + 2, and JL = 5x – 10 JK + KL = JLJKL JK + KL = JL
32. Table of ContentsConcept 5: Bisector, Midpoint and Distance Formula Examples
33. Back 3
34. BackM( , ) A(-4, 1)B(2, 4)C(1, 1)D(5, -5)M = ( , ) M = ( , ) M = (-1, ) M = ( , ) M = ( , ) M = (3, )
35. Back A(-3, 5)B(2, 3) C(-4, -4)B(4, -1)
36. Table of ContentsDistance ExamplesUse the number line to find each measure.1. LN 2. JLFind the distance between each pair of points. 3. 4. C(–3, –1), Q(–2, 3) MoreLN = |3 - 9| = |-6| = 6JL = |-5 - 3| = |-8| = 8FG = = = = CQ = = = =
37. Table of ContentsMidpoint ExamplesUse the number line to find the coordinate of the midpoint of each segment.5. 6. Find the coordinates of the midpoint of a segment with the given endpoints. 7. T(3, 1), U(5, 3) 8. J(-4, 2), F(5, -2) Find the coordinates of the missing endpoint if P is the midpoint of .9. N(2, 0), P(5, 2) 10. N(5, 4), P(6, 3) DE = = = 9 BC = = = 1 M = ( , ) = ( , ) = (4, 2) M = ( , ) = ( , ) = ( , 0)
38. Table of ContentsConcept 6: AnglesExamples
39. Backtwo rays with the same initial point, measured in degrees.Named by its vertex or the 3 letters on it with the middle letter being the vertex.An angle that measures less than 90 degrees but greater than 0 degrees.An angle that measures greater than 90 degrees but less than 180 degrees.An angle that measures exactly 90 degrees.An angle that measures exactly 180 degrees.Two or more angles that have the same measure.
40. Back Acute angleRight angleObtuse angle Angle names:Vertex:Sides:Point B Point EPoint S
41. Back E
42. BackPSRT = 18 = x = 28 = x
43. Table of ContentsAngle BisectorsExamples 3x + 255x - 10 2 17.5 17.5 3(17.5) +25 52.5 +25 77.5 77.5 5(17.5) -10 87.5 -10 77.5 77.5 + + 77.5 180 -
44. Back 9 = x x = 13
45. Table of ContentsExamples
46. Table of ContentsConcept 7: Angle PairsExamples
47. Back90 (6) – 2 66 – 2 64 (6) – 4 30 – 4 26
48. Back180 (11) + 9 88 + 9 97 (11) + 17 66 + 17 83
49. Backvertexsideyesyesyesnono
50. Backnoyesyesyesno
51. Backnononoyesno
52. Table of ContentsExamplesFor Exercises 1 – 6, use the figure at the right. Name an angle or angle pair that satisfies each condition.Name two acute vertical angles.Name two obtuse vertical angles.Name a linear pair.Name two acute adjacent angles.Name an angle complementary to EKH.Name an angle supplementary to More and and and and and and and and
53. Table of ContentsExamplesFor Exercises 1 – 6, use the figure at the right. Name an angle or angle pair that satisfies each condition.Find the measures of an angle and its complement if one angle measures 24 degrees more than the other. The measure of the supplement of an angle is 36 less than the measure of the angle. Find the measures of the angles.More
54. Table of ContentsMore ExamplesFor exercises 9 – 10, use the figure at the right.9. If , find the value of x so that . 10. If and , find the value of y so that is a right angle. Yes, because there is a right angle mark.Yes, because they make a straight angle.No, because they don’t share a common side.
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