Name_________________________________________________ Date ________________ Class_____________
Lesson 2.4: Using Postulates and Diagrams
GOAL: Use familiar postulates involving points, lines, and planes to draw and interpret diagrams.
New Vocabulary: A line is a line perpendicular to a plane if and only if the line intersects the plane in
a point and is perpendicular to every line in the plane that intersects it at that point.
Symbol for Perpendicular Figures:
Example: Write using symbols, “the line through points L and
M is perpendicular to a line segment with endpoints P and Q:
Familiar Postulates:
Through any two points there exists exactly one line.
A line contains at least two points.
If two lines intersect, then their intersection is exactly one point.
Through any three noncollinear points there exists exactly one plane.
A plane contains at least three noncollinear points.
If two points lie in a plane, then the line containing them lies in the plane.
If two planes intersect, then their intersection is a line.
Now, complete the example problems in your notes with a partner.
Independent Practice
Use the diagram to write an example of each postulate.
1.
Through any two points there exists exactly one line.
2. A line contains at least two points.
3. If two lines intersect, then their intersection is exactly one point.
4. Through any three noncollinear points there exists exactly one plane.
5. A plane contains at least three noncollinear points.
6. If two points lie in a plane, then the line containing them lies in the plane.
7. If two planes intersect, then their intersection is a line.
Sketch a diagram showing the given information.
8.
AB
10. LN
BC
plane A and plane A bisects LN
9.
Line m bisects ST
11. Plane G intersects plane H in EF , point D
lies in plane G, DE plane H.
Can the statement be assumed to be true from the diagram? Explain why or why not.
GA
AD
12. AB and AD are opposite rays.
13.
BAC and CAD are supplementary.
14.
BAC
15. CE
BAE
plane S
16. BD lies in plane S and in plane T
17. If G is a point in plane S, then CG lies in S.
18. CE bisects BD
19. Plane T bisects BD .