12.3 - 12-3 The Basic Proportionality Theorem and Its...

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Unformatted text preview: 12-3 The Basic Proportionality Theorem and Its Converse A) 12-2 (The Basic Proportionality Theorem) a. If a line parallel to one side of a triangle intersects the other two sides in distinct points, then it cuts off segments which are proportional to these sides b. Proof: Given: Prove: 1) base is ________, base is __________ What do we know about their altitudes? Therefore, there ratio of their bases is the ratio of their areas 2) base is _________, base is ____________ What do we know about their altitudes? Therefore, there ratio of their bases is the ratio of their areas 3) What can we say about the bases/altitude of and Therefore, 4) Putting all three together, what do we get? 5) add 1 to both sides of the equation, what does that give us? B) Other proportions from this basic proportion a. C) Theorem 12-3 a. If a line intersects two sides of a triangle, and cuts off segments proportional to these two sides, then it is parallel to the third side b. If Proof: Given: triangle ABC and Prove: 1) Let be the line through B and parallel to Therefore, 2) But by hypothesis we know, 3) Therefore, And D) Example a. # 11 from homework Prove the Angle Bisector Proportionality Theorem : The bisector of an angle of a triangle separates the opposite side into segments whose lengths are proportional to the lengths of the adjacent sides. Given: bisects D is on Prove: 1) Introduce parallel to 1) line postulate 2) 2) 3) 3) 4) 4) 5) 6) 7) 8) #15 from the homework 5) 6) 7) 8) Prove the Parallels Proportional Segment Theorem: If three or more parallels are each cut by two transversals are proportional. Given: transversals and cut parallels and in A, B, C and D, E, F respectively Prove: 1) Introduce and let G be the intersection of and 1) 2) 3) 4) 2) 3) 4) ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State University.

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12.3 - 12-3 The Basic Proportionality Theorem and Its...

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