Download Unit 2.1b

UNIT 2: REASONING AND PROOF
2.1b – Conditional Statements with Postulates
MA30: GEOMETRY
(Text Ref: Ch 2.1 Pg 71-78)
I. Point & Line Postulates
For Postulates 5 - 6, write a short paragraph that describes each postulate. Use the diagram
to the write as a reference.
Postulate 5: Through any __________ there exists exactly one line.
Postulate 6: A __________ contains at least two points.
Postulate 7: If two lines intersect, then their intersection is exactly __________.
II. Point, Line & Plane Postulates
For Postulates 8 - 11, write a short paragraph that describes each
postulate. Use the diagram to the write as a reference.
Postulate 8:
Through any __________ noncollinear points there
exists exactly __________ plane.
Postulate 9:
A plane contains at least three ___________ points.
Postulate 10
If two points lie in a plane, then the ______ containing them _______ in the plane.
Postulate 11
If __________ planes intersect, then their intersection is a __________.
2.1b – Conditional Statements with Postulates (continued)
III. Using Postulates and Counterexamples
A. Decide whether the statement is true or false. Justify your answer
by stating the counterexample.
1) “Through any three points there exists exactly one line.”
2) “For any one point in a plane, there exists exactly one line
through that point in that plane.”
B. Decide whether the statement is true or false. Justify your answer.
1) A line can be in more than one plane.
2) Four noncollinear points are always coplanar.
3) Two nonintersecting lines can be non-coplanar.
C. Rewriting a Postulate - Postulate 5
1) Rewrite Postulate 5 in if-then form.
2) Write the inverse, converse, and contrapositive of Postulate 5.
D. Rewriting a Postulate - Postulate 11
1) Rewrite Postulate 11 in if-then form.
2) Write the inverse, converse, and contrapositive of Postulate 11.