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Explore the validity of geometry postulates with explanations and examples. Learn how to determine the truth or falsity of statements based on definitions and previous knowledge. Includes exercises and solutions.
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Week 6 Warm Up 09.22.11 1) State the postulate that shows the statement to be false: A line contains at least three points.
Definitions Previous knowledge used to explain your answers. Ex 1 Is the statement true or false: • A Explain. • • X B D D,X, and B are collinear. • C Answer True. 2 or more points are collinear if they lie on the same line. D,X, and B all lie on DB so they are collinear.
Do 1: True or False: ∠ AXB is adjacent to ∠ CXD • A 1st Sentence: True or False 2nd Sentence: Definition 3rd Sentence: Describe why definition proves the graph • • X B D • Answer False. By definition adjacent angles must share a common side. ∠ AXB and ∠ CXD do not share a common side so they are not adjacent. C
Biconditional Statement A statement that contains the phrase “if and only if”. It is a conditional statement and its converse. Ex 3 Three lines are coplanar if and only if theylie in the same plane. Conditional Statement: if three lines are coplanar, then they lie in the same plane. Converse: if three lines lie in the same plane then they are coplanar.
• A Do: 2 ∠ AXB is vertical to ∠ BXC • • X B D • C Assignment: Textbook Page 82, 13 – 23 All and 59 – 68 All.