NAME
2-5
DATE
PERIOD
Practice
Postulates and Paragraph Proofs
Explain how the figure illustrates that each statement
is true. Then state the postulate that can be used to show
each statement is true.
+
3
1. The planes J and K intersect at line m.
The two planes meet on the line m. Postulate: If two
planes intersect, then their intersection is a line.
2. The lines l and m intersect at point Q.
2
m
1
,
The point Q lies on line m and line l. Postulate: If two
lines intersect, then their intersection is exactly one point.
Determine whether the following statements are always, sometimes, or never true.
Explain.
3. The intersection of two planes contains at least two points.
Always; the intersection of two planes is a line, and a line contains at
least two points.
4. If three planes have a point in common, then they have a whole line in common.
Sometimes; they might have only that single point in common.
⎯⎯ lie in plane A . State the postulate
In the figure, line m and TQ
that can be used to show that each statement is true.
Postulate 2.5: If two points lie in a plane, then the
entire line containing those points lies in that plane.
T
L
m A
Q
intersect at T.
6. Line m and ST
Postulate 2.6: If two lines intersect, then their intersection
is exactly one point.
−−
−−−
7. In the figure, E is the midpoint of AB and CD, and AB = CD. Write a
−− −−−
paragraph proof to prove that AE ED.
C
A
E
−−
−−
Given: E is the midpoint of AB and CD.
AB = CD
D
−− −−
Prove: AE ED
−−
−−
Proof: Since E is the midpoint
of
AB
and
CD, we know by the Midpoint
−− −−
−− −−
Theorem, that AE EB and CE ED. By the definition of congruent
1
1
AB and CE = ED = − CD. Since, AB = CD,
segments, AE = EB = −
2
2
1
1
−
AB = −
CD by the Multiplication Property. So AE = ED, and by the
2
2
−−
−−
definition of congruent segments AE ED.
B
8. LOGIC Points A, B, and C are noncollinear. Points B, C, and D are noncollinear. Points
A, B, C, and D are noncoplanar. Describe two planes that intersect in line BC.
The plane that contains A, B, and C and the plane that contains B, C,
and D
Chapter 2
34
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Points L, and T and line m lie in the same plane.
S