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Contents Lesson 2-1Inductive Reasoning and Conjecture Lesson 2-2Logic Lesson 2-3Conditional Statements Lesson 2-4Deductive Reasoning Lesson 2-5Postulates and Paragraph Proofs Lesson 2-6Algebraic Proof Lesson 2-7Proving Segment Relationships Lesson 2-8Proving Angle Relationships

Lesson 5 Contents Example 1Points and Lines Example 2Use Postulates Example 3Write a Paragraph Proof

Example 5-3a Prove: ACD is a plane. Given intersecting, write a paragraph proof to show that A, C, and D determine a plane. Given: intersects Proof: must intersect at C because if two lines intersect, then their intersection is exactly one point. Point A is on and point D is on Therefore, points A and D are not collinear. Therefore, ACD is a plane as it contains three points not on the same line.

Example 5-3b Given is the midpoint of and X is the midpoint of write a paragraph proof to show that

Example 5-3c Proof: We are given that S is the midpoint of and X is the midpoint of By the definition of midpoint, Using the definition of congruent segments, Also using the given statement and the definition of congruent segments, If then Since S and X are midpoints, By substitution, and by definition of congruence,

End of Lesson 5

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