2.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Postulates and Diagrams

2.4 Warm-Up State which postulate justifies each statement. 2. If M is between X and Y, then XM + MY = XY. ANSWERAngle Addition Postulate ANSWER Segment Addition Postulate 1. If D is in the interior of ABC, then m ABD + m DBC = m ABC.

2.4 Warm-Up State which postulate justifies each statement. ANSWER Find the measure of MN if N is between M and P, MP = 6x – 2, MN = 4x, and MP = 16.

2.4 Example 1 State the postulate illustrated by the diagram. a.a. b.b. SOLUTION a.a. Postulate 7 : If two lines intersect, then their intersection is exactly one point. b.b. Postulate 11 : If two planes intersect, then their intersection is a line.

2.4 Example 2 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. SOLUTION

2.4 Guided Practice Which postulate allows you to say that the intersection of plane P and plane Q is a line? 1. ANSWER Postulate 11 Use the diagram. Write examples of Postulates 5, 6, and ANSWER 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

2.4 Example 3 SOLUTION Sketch a diagram showing TV intersecting PQ at point W, so that TW WV. Draw TV and label points T and V. STEP 1 Draw point W at the midpoint of TV Mark the congruent segments. STEP 2 Draw PQ through W. STEP 3

2.4 Example 4 Which of the following statements cannot be assumed from the diagram? SOLUTION A, B, and F are collinear. E, B, and D are collinear. AB plane S CD plane T 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.

2.4 Guided Practice 3. If the given information stated PW and QW are congruent, how would you indicate that in the diagram? In Exercises 3 and 4, refer back to Example 3. ANSWER Sketch a diagram showing TV intersecting PQ at point W, so that TW WV. Example 3:

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

2.4 Guided Practice 5. In the diagram for Example 4, can you assume plane S intersects plane T at BC ? ANSWERYes 6. Explain how you know that AB BC in Example 4. 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

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

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

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