1) The document discusses geometry postulates and using diagrams to illustrate and apply postulates. It provides examples of writing statements that illustrate specific postulates based on diagrams. 2) Students are asked to identify which postulate a diagram or statement illustrates. One example asks which postulate allows you to say that the intersection of two planes is a line. 3) The document contains guided practice problems asking students to write statements applying specific postulates based on diagrams, and questions testing understanding of concepts like intersections of lines and planes.

1. 2.42.4 Use Postulates and Diagrams
Bell 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. 2.4

3. 2.4Example 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 their
intersection is a line.

4. 2.4Example 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

5. 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

6. 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 .

7. 2.4

8. 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.

9. 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

10. 2.4Exit Slip
1. 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.

11. 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
ANSWER true
4. GH lies in plane M.
ANSWER false
5. ABE and HED are vertical angles.
Exit Slip

12. 2.4
Homework
Pg 101-104
#20, 21, 22, 23, 41