Sec 1 5 Measuring Segments Objectives 1 Finding

Sec. 1 – 5 Measuring Segments Objectives: 1) Finding the lengths of segments.

Geometry vs Algebra Segments are Congruent – Symbol [ ] – AB CD – 1 2 Lengths of segments are equal. – Symbol [ = ] – AB = CD – m 1 = m 2 =

Ruler Postulate P(1 – 5) The points of a line can be put into one–to–one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. A AB B a b Coordinate of A Coordinate of B AB = a – b The measure of the length of the segment AB (It’s a number) 1 cm 4 cm

Ex. 1: Find AB, CE, & AC A -8 C -6 B -4 AB = -8 – 5 -2 0 CE = -5 – 6 2 E 4 6 AC = -8 – -5 = -13 = -11 = -8 + 5 = 13 = 11 = -3 = 3 8

Segment Addition Postulate P (1 – 6) If 3 points A, B, & C are collinear & B is between A & C, then AB + BC = AC B A C

Ex. 2: Find the length of the missing segment L M N 15 Find MN if – LN = 20 – LM = 15 LM + MN = LN 20 D Find DS if – DT = 60 – DS = 2 x – 8 – ST = 3 x – 12 S 2 x - 8 15 + MN = 20 T MN = 5 3 x - 12 60 DS + ST = DT DS = 2 x – 8 (2 x - 8) + (3 x -12) = 60 DS = 2(16) – 8 5 x – 20 = 60 DS = 24 x = 16

Midpoint – Is a point that divides a segment into two parts. R RS ST RS = ST S T Ex. 3: Find AC & CB if C is the Midpoint of AB. – AC = 2 x + 1 – CB = 3 x – 4 A C B AC = 2 x + 1 AC = CB AC = 2(5) + 1 2 x + 1 = 3 x – 4 CB = AC = 11 5=x

What have we learned? ? Finding the length of segments: D -5 E 0 3 DE = -5 – 3 = 8 Segment Addition: MN + NP = MP (5 x – 4) + (2 x + 14) = 80 7 x + 10 = 80 x = 10 M N 5 x - 4 P 2 x + 14 80