1-3: Measuring Segments

Today’s Objectives  Use The Ruler Postulate to calculate lengths of segments  Identify the midpoint of a segment, and apply its properties to solve the length of a segment  Differentiate between congruent segments and equal distances

Ruler Postulate  Postulate 1-5  Every point on a line can be paired with a real number  One-to-one correspondence A B

Example  Find the distance between the following points.  A and B  B and C  A and D A B C D AB = 6 BC = 4 AD = 14

Segment Addition Postulate  Postulate 1-6  If three points A, B, and C are collinear, and B is between A and C, then AB + BC = AC A B C AB + BC = AC

Example  If EG = 59, what are EF and FG? E G F 8x-14 4x+1 Set Up an Equation EF + FG = EG (8x-14) + (4x+1) = 59 8x x+1 = 59 12x -13 = 59 12x = 72 x = 6 8(6) – 14 4(6)+1 48 – EF = 34 EG = 25

Congruent Segments  Congruent Segments – two segments with the same length  Congruent is not the same as equal! A B D C

Example  What segments are congruent? A B C D Congruent Segments Equal Distances

Midpoint  Midpoint – the point that divides the segment into two congruent segments A M B Congruent Segments Equal Distances

Midpoint Example R P C A B Cut in half