2.4 Use Postulates and Diagrams - Mr. Hubarth's Website
2.4 Use Postulates and Diagrams Hubarth Geometry Postulates Point, Line and Plane Postulates Postulate 5 Postulate 6 Postulate 7 Postulate 8 Postulate 9 Postulate 10 Postulate 11 Through any two points there exists exactly one line. A line contains at least two points. If two lines intersects, then their intersection is exactly one point.
Through any three noncollinear points there exists exactly one plane. A plane contains at least three noncollinear points. If two points lie in a plane, then the line containing them lies in the plane. If two planes intersect, then their intersection is a line. Ex 1 Identify a Postulate Illustrated By a Diagram State the postulate illustrated by the diagram. a. b. a. Postulate 7: If two lines intersect, then their intersection is exactly one point. b. Postulate 11: If two planes intersect, then their intersection is a line. Ex 2 Identify Postulates from a Diagram
Use the diagram to write examples of Postulates 9 and 10. Postulate 9: Plane P contains at least three noncollinear points, A, B, and C. Postulate 10: Point A and point B lie in plane P, so line n containing A and B also lies in plane P. Interpreting Diagrams When you interpret a diagram, you can assume information about size or measure only if it is marked. You Can Assume All points shown are coplanar You Cannot assume G,
F, andE are collinear AHBand BHD are a linear pair AHF and BHD are vertical angles. A, H, J and D are collinear AD and BF intersect at H. . . B G P
.C H A . BF and CE intersect. BF and CE do not intersect [email protected] AD^ BF or mAHB=90 J
. F .E . D Ex 3 Use Given Information To Sketch a Diagram Sketch a diagram showing TV intersecting PQ at point W, so that TW @WV. Ex 4 Interpret Diagram in Three Dimensions
Which of the following statements cannot be assumed from the diagram? A, B, and F are collinear. E, B, and D are collinear. AB ^ plane S AF intersects BC at point B No drawn line connects E, B, and D, so you cannot assume they are collinear. With no right angle marked, you cannot assume CD ^plane T. Practice 1. Which postulate allows you to say that the intersection of plane P and plane Q is a line? Postulate 11
2. Use the diagram, to write examples of Postulates 5, 6, and 7. Postulate 5 Line n passes through points A and B Postulate 6 Line n contains A and B Postulate 7 Line m and n intersect at point A 3. If the given information stated PW and QW are congruent, how would you indicate that in the diagram? 4. Name a pair of supplementary angles in the above diagram. Explain. TWP and VWP TWQ and VWQ
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