Geometry 1 2 Segments and their Measures TopicObjectives

Geometry 1. 2 Segments and their Measures

Topic/Objectives: • Use segment postulates • To compare segments Geometry 1. 2 Segments and Their Measure 19 January 2022 2

A rule that is accepted without proof. Sometimes are called an Axiom. Geometry 1. 2 Segments and Their Measure 19 January 2022 3

Rule that is proved. Geometry 1. 2 Segments and Their Measure 19 January 2022 4

Postulate 1: Ruler Postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. A B x 1 x 2 coordinates Geometry 1. 2 Segments and Their Measure 19 January 2022 5

Ruler Postulate continued The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. A B x 1 x 2 AB = |x 1 – x 2| = |x 2 – x 1| Geometry 1. 2 Segments and Their Measure 19 January 2022 6

Reminder B A AB is the name of this segment. AB is the length of this segment. Distance Picky? Yes – but in this text, very important! Geometry 1. 2 Segments and Their Measure 19 January 2022 7

WARNING! • In Algebra, AB means A B. • In Geometry, AB is the length of a segment whose endpoints are the points A and B. • AB is the segment, AB is its length. Geometry 1. 2 Segments and Their Measure 19 January 2022 8

Example R S 3 5. 5 Find RS Solution: NOTICE: RS is the length of segment RS. It is incorrect to write RS = 2. 5 RS = |5. 5 – 3| = |2. 5| = 2. 5 or = |3 – 5. 5| = |-2. 5| = 2. 5 Geometry 1. 2 Segments and Their Measure 19 January 2022 9

Betweeness A D B C B is between A and C. D is NOT between A and C. A, B, and C are collinear, A, D, and C are not collinear. Geometry 1. 2 Segments and Their Measure 19 January 2022 10

Segment Addition Postulate 2 If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C. A B AB C BC AC Geometry 1. 2 Segments and Their Measure 19 January 2022 11

Geometry 1. 2 Segments and Their Measure 19 January 2022 12

Sample Problem M P N If MN = 10, and MP = 24. 5, find NP. Solution Notice: By SAP, MN + NP = MP DO NOT WRITE so 10 + NP = 24. 5 MN + NP = MP and NP = 14. 5 Geometry 1. 2 Segments and Their Measure 19 January 2022 13

SAP can be extended… A B C D AB + BC + CD = AD Geometry 1. 2 Segments and Their Measure 19 January 2022 14

Your turn. Do this problem. RA = 8 T 5 A R 8 S 7 20 By SAP: TS = 5 RS = 20 Find AT 8 + AT + 5 = 20 AT + 13 = 20 AT = 7 Geometry 1. 2 Segments and Their Measure 19 January 2022 15

A More Complex Problem First, draw this figure. A AB = 3 CD = 10 B C D E F Find BC and DE. AD = 20 EF = 5 AF = 31 Geometry 1. 2 Segments and Their Measure 19 January 2022 16

Solution 3 A AB = 3 CD = 10 AD = 20 EF = 5 AF = 31 7 B 10 C 5 6 D E F 1. Label what we know. 2. AD is 20, so BC must be… 7 3. AF is 31. The parts we have total 25. So DE must be… 6 Geometry 1. 2 Segments and Their Measure 19 January 2022 17

Sample Problem D 30 O 25 G DO = 4 x + 10 Solution. By SAP: OG = 2 x + 15 DO + OG = DG DG = 55 (4 x + 10) + (2 x + 15) = 55 Solve for x. 6 x + 25 = 55 Then find DO and OG. 6 x = 30 x=5 Geometry 1. 2 Segments and Their Measure DO = 4(5) + 10 = 30 OG = 2(5) + 15 =1925 January 2022 18

C CA = 3 x + 12 AT = 2 x – 2 CT = 25 Your turn… A T Solution: (3 x + 12) + (2 x – 2) = 25 5 x + 10 = 25 5 x = 15 Find x, CA, and AT. x = 3 CA = 3(3) + 12 = 21 AT = 2(3) – 2 = 4 Geometry 1. 2 Segments and Their Measure 19 January 2022 19