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Measuring Segments and Angles During this lesson, you will use segment postulates to determine the lengths of segments.
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A coordinate is a point’s Segment Vocabulary distance and direction from 0 on a number line Ex. Point A is Point B is AB = _____units -2 0 3 AB Read: “the measure of line segment AB = 5” 2 units left of 0 3 units right of 0 5
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Ruler Postulate The points on a line can be put into a one- to-one correspondence with the real numbers so that the distance between any two numbers _________________ ______________________________. is the absolute value of their difference. -2 0 3 AB AB = │ -2-3 │ = _____ Ex.
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Use AB CD (bar on top) when referring to the actual segments. Notation for congruent segments: Congruent ( ) segments are segments with the same length. Use AB = CD (no bar on top) when referring to the lengths (or #’s). Read: “segment AB is congruent to segment CD” Read: “ measure of segment AB is equal to measure of segment CD”
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Actual segments A B C D A B C D 2cm. AB = CD Lengths (or numbers) AB CD mAB = mCD
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A midpoint is a point that ______ ____________________________. divides a segment into two segments. QR RS Q SR R is the midpoint of QS therefore: m QR = m RS QR = RS
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A B C POSTULATE Segment Addition Postulate If three points A, B and C are collinear and B is between A and C, then AB + BC = AC
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2x - 8 3x - 12 D S T Substitute Solve for x DS + ST = DT 2x - 8 + 3x - 12 = 60 5x - 20 = 60 5x = 80 x = 16 DS = 2x - 8 ST = 3x - 12 DS = 2(16) - 8 DS = 24 ST = 36 Ex. #1 If DT = 60, find the value of x. Then find DS and ST. Segment Addition Postulate ST = 3(16) - 12
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EX. #2 Comparing Segment Lengths Compare AD and BF. Compare BD and EG. 0 3 5 7 8 -2 -6 ABCDEFG AD = 9 BF = 9 So, AD = BF B D = 5 EG = 3 So, BD > EG
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EX. #3 Using the Midpoint M is the midpoint of RT. Find RM, MT and RT. R M T Def. of midpt. 5x + 9 8x - 36 RM = MT Substitute 5x + 9 = 8x - 36 Solve for x 45 = 3x 15 = x RM = 5x + 9 RM = 5(15) + 9 RM = 84 = MT RT = 84 + 84 = 168
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C D A B Final Checks for Understanding 1.What is a postulate? 2.Draw a sketch of three collinear points. Label them. Then write the Segment Addition Postulate for the points. 3.Use the diagram. How can you determine BD if you know BC and CD?
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Homework Assignment: Pages 29-33, text: #1-15, 29-32, 42-46, 71-72
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