Section 1 - 3 Measuring Segments

Things You Might Already Know Coordinate A numerical location Can be given in one of three ways A single relative marker (for linear use) An ordered pair (x ,y) (for planar use) An ordered triple (x, y, z) (for spatial use) Distance The linear difference between two coordinates You have to subtract

Your First Formula To determine a segment length Where AB is the segment in question a and b are the numerical coordinates A B b a

Your First Formula Example Determine the length of segment ST Find the length of segments UV and SV S -2 -4 12 14 2 4 10 U 8 6 T V

A Sprinkle of Algebra The Segment Addition Postulate AB + BC = AC Find AC if AB = 4 and BC = 7 AC = 11 Find AB if AC = 14 and BC = 6 AB = 8 BIG TIP  When given a drawing, do not base assumptions on the drawing itself. Instead use what is on the drawing. A B C

Example 1 If EG = 59, find EF and FG Use the Segment Addition Postulate EF + FG = EG 8x – 14 + 4x + 1 = 59 12x – 13 = 59 + 13 +13 12x = 72 12 12 x = 6

But Wait, There’s More Now we must find what we were asked for EF = 8x – 14 EF = 8(6) – 14 EF = 48 – 14 EF = 34 FG = 59 – 34 FG = 25

Example 2 If EG = 120, find EF and FG Use the Segment Addition Postulate EF + FG = EG 4x + 6+ 7x + 15 = 120 11x + 21 = 120 - 21 -21 11x = 99 11 11 x = 9

Example 2 cont. EF = 4x + 6 EF = 4(9) + 6 EF = 36 + 6 EF = 42 FG = 120 – 42 FG = 78

A Potential Shortcut Congruence On a Number Line Congruent is the adjective Two or more associated figures are identical The symbol for congruent is On a Number Line Are TU and UV congruent? S -2 -4 12 14 2 4 10 U 8 6 T V

A Potential Shortcut Use Distance to check for congruence Since both distances are the same, the segments are congruent

The Use Bisect To cut in half To cut into two congruent parts If the bisecting is done by a point, it is referred to as a midpoint Mathematically, the two segments are equal to each other

Example 3 Find PR if Q is the midpoint Set the segments equal to each other PQ = QR 6x – 7 = 5x + 1 + 7 + 7 6x = 5x + 8 -5x -5x x = 8 PQ = 6x – 7 PQ = 6(8) – 7 PQ = 48 – 7 PQ = 41 PR = 2PQ PR = 82 6x – 7 5x + 1 P Q R

Assignment Pg 24 8 - 28