EXAMPLE 1
Identify a postulate illustrated by a diagram
State the postulate illustrated by the diagram.
b.
a.
SOLUTION
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 2
Identify postulates from a diagram
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.
GUIDED PRACTICE
for Example 1 and 2
1. Use the diagram in Example 2. Which postulate
allows you to say that the intersection of plane P
and plane Q is a line?
ANSWER
Postulate 11
GUIDED PRACTICE
for Example 1 and 2
2. Use the diagram in Example 2 to write examples of
Postulates 5, 6, and 7.
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
EXAMPLE 3
Use given information to sketch a diagram
Sketch a diagram showing TV intersecting PQ at point
W, so that TW
WV .
SOLUTION
STEP 1
Draw TV and label points T and V.
STEP 2
Draw point W at the midpoint of TV
Mark the congruent segments.
STEP 3
Draw PQ through W.
EXAMPLE 4
Interpret a diagram in three dimensions
Which of the following
statements cannot be assumed
from the diagram?
A, B, and F are collinear.
E, B, and D are collinear.
AB plane S
CD plane T
AF intersects BC at point B.
SOLUTION
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.
GUIDED PRACTICE
for Examples 3 and 4
In Questions 3 and 4, refer back to Example 3.
3.
If the given information stated PW and QW are
congruent, how would you indicate that in the
diagram?
ANSWER
GUIDED PRACTICE
4.
for Examples 3 and 4
Name a pair of supplementary angles in the
diagram. Explain.
ANSWER
In the diagram the angle TWP and VWP form a
linear pair So, angle TWP, VWP are a pair of
supplementary angles.
GUIDED PRACTICE
5.
for Examples 3 and 4
In the diagram for Example 4, can you assume
plane S intersects plane T at BC ?
ANSWER
Yes
GUIDED PRACTICE
6.
for Examples 3 and 4
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
Daily Homework Quiz
1.
For use after Lesson 2.4
Use the diagram to write an example of Postulate 7.
ANSWER
Line m intersects line n in point F and no other point.
Daily Homework Quiz
2.
For use after Lesson 2.4
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.
Daily Homework Quiz
For use after Lesson 2.4
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
Daily Homework Quiz
For use after Lesson 2.4
Use the diagram to determine if the statement is true
or false.
4.
GH lies in plane M.
ANSWER
true
Daily Homework Quiz
For use after Lesson 2.4
Use the diagram to determine if the statement is true
or false.
5.
ABE and
ANSWER
false
HED are vertical angles.