Measuring Segments and Angles During this lesson, you will use segment postulates to determine the lengths of segments.

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Presentation transcript:

Measuring Segments and Angles During this lesson, you will use segment postulates to determine the lengths of segments.

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 AB Read: “the measure of line segment AB = 5” 2 units left of 0 3 units right of 0 5

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 AB AB = │ -2-3 │ = _____ Ex.

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”

Actual segments A B C D A B C D 2cm. AB = CD Lengths (or numbers) AB  CD mAB = mCD

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

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

2x - 8 3x - 12 D S T Substitute Solve for x DS + ST = DT 2x x - 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

EX. #2 Comparing Segment Lengths Compare AD and BF. Compare BD and EG ABCDEFG AD = 9 BF = 9 So, AD = BF B D = 5 EG = 3 So, BD > EG

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 = = 168

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?

Homework Assignment: Pages 29-33, text: #1-15, 29-32, 42-46, 71-72