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Warm Up

Use Postulates and Diagrams. Warm Up. Lesson Presentation. Lesson Quiz. 1. If D is in the interior of ABC , then m ABD + m DBC = m ABC. ANSWER. Angle Addition Postulate. Segment Addition Postulate. ANSWER. Warm-Up. State which postulate justifies each statement.

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Warm Up

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  1. Use Postulates and Diagrams Warm Up Lesson Presentation Lesson Quiz

  2. 1. IfD is in the interior ofABC, then m ABD + m DBC = m ABC. ANSWER Angle Addition Postulate Segment Addition Postulate ANSWER Warm-Up State which postulate justifies each statement. 2.If Mis between Xand Y, then XM + MY = XY.

  3. 12 ANSWER Warm-Up State which postulate justifies each statement. 3. Find the measure of MNif Nis between Mand P,MP= 6x – 2, MN = 4x, and MP = 16.

  4. b. a. 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. Example 1 State the postulate illustrated by the diagram. SOLUTION

  5. Example 2 Use the diagram to write examples of Postulates 9 and 10. SOLUTION Postulate 9: Plane Pcontains at least three noncollinear points, A, B, and C. Postulate 10: Point Aand point Blie in plane P, so line ncontaining Aand Balso lies in plane P.

  6. 2. Write examples of Postulates 5, 6, and 7. 1. Which postulate allows you to say that the intersection of plane Pand plane Qis a line? ANSWER Postulate 11 ANSWER Postulate 5 : Linenpasses through pointsAandB Postulate 6 : LinencontainsAandB Postulate 7 : Linemand n intersect at pointA Guided Practice Use the diagram.

  7. Sketch a diagram showing TVintersecting PQat point W, so that TWWV. STEP 1 Draw TVand label points Tand V. STEP 2 Draw point Wat the midpoint of TVMark the congruent segments. STEP 3 Draw PQthrough W. Example 3 SOLUTION

  8. Which of the following statements cannot be assumed from the diagram? ABplane S CDplane T AFintersects BCat 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 CDplane T. Example 4 A, B, and Fare collinear. E, B, and Dare collinear. SOLUTION

  9. Example 3: 3. If the given information stated PWand QWare congruent, how would you indicate that in the diagram? Sketch a diagram showing TVintersecting PQat point W, so that TWWV. ANSWER Guided Practice In Exercises 3 and 4, refer back to Example 3.

  10. 4. Name a pair of supplementary angles in the diagram. Explain. ANSWER Sample answer:TWP, VWP; they form a linear pair. Guided Practice In Exercises 3 and 4, refer back to Example 3.

  11. 5. In the diagram for Example 4, can you assume plane Sintersects plane Tat BC? 6. Explain how you know that ABBCin Example 4. ANSWER Yes ANSWER It is given that line AB is perpendicular to plane S, therefore line AB is perpendicular to every line in the plane that intersect it at point B. So, AB BC Guided Practice

  12. 1. Use the diagram to write an example of Postulate 7. ANSWER Line m intersects line n in point F and no other point. Lesson Quiz

  13. 2. Decide whether the statement “Two planes can intersect in exactly one point R” is true or false. If false, give a reason. ANSWER False; Postulate 11 says that if two planes intersect, their intersection is a line. Lesson Quiz

  14. 3. The intersection of planes M and N is points B, E and H. ANSWER false 4. 5. GH lies in plane M. ABE and HED are vertical angles. ANSWER true ANSWER false Lesson Quiz Use the diagram to determine if the statement is true or false.

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