2.42.4 Use Postulates and DiagramsBell Thinger

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.

ANSWER 36

3. Find the measure of MN if N is between M and P, MP = 6x – 2, MN = 4x, and NP = 16.

2.4

2.4Example 1State 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.

2.4Example 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

2.4Guided 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

2.4Example 3

SOLUTION

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

Sketch a diagram showing TV intersecting PQ at point W, so that TW WV .

2.4

2.4Example 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.

2.4Guided Practice

3. Can you assume plane S intersects plane T at BC ?

ANSWER Yes

4. Explain how you know that AB BC.

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

2.4Exit Slip1. Use the diagram to write an example of Postulate 7.

ANSWER Line m intersects line n in point F and no other point.

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.

2.4Use 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.

Exit Slip

2.4

Homework

Pg 101-104 #20, 21, 22, 23, 41