2.4

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson 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.

ANSWER Angle 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 12

3. 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. b.

SOLUTION

a. Postulate 7: If two lines intersect, then their intersection is exactly one point.

b. Postulate 11: If two planes intersect, then theirintersection is a line.

2.4 Example 2

Use the diagram to write examples of Postulates 9 and 10.

Postulate 9: Plane P contains atleast 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 7.2.

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 3.

4. 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 ?

ANSWER Yes

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.

ANSWER false

ANSWER true

4. GH lies in plane M.

ANSWER false

5. ABE and HED are vertical angles.