Betweeness & Collinearity

Lesson6:

Review: Identify the collinear points

Problem of the day!

Given two distinct points, how many lines can be drawn?

AC

Presentation

Show a number line as given:

Give the coordinate of points

BetweenessThe concept of betweeness is

applied to points and segments, since a segment is determine by two (2) points.

Point B is between points A and C, while point D is not between points A and C. Point A, B, and C are collinear, since they lie on the same line.

Betweeness refers only to collinear points.

DA B C

By definition

Point B is between points A and C if and only if B, A and C are collinear and

.Addition Postulate: If B is between A and C, then

Illustrative Example #1:

Points A, B and C are collinear. If AB = 12, BC = 47 and AC = 35, determine which point is between the other two.

Solution:

Points A, B and C are collinear. If AB = 12, BC = 47 and AC = 35, determine which point is between the other two.Check to which two measures add to equal the third

12 + 35 = 47 A is between B and C.

If QS = 29, QT = 52, find ST

RP Q S

RP Q S T

Illustrative Example #2:

Solution

If QS = 29, QT = 52, find ST

RP Q S TIf QS = 29 and QT = 52 find STQS + ST = QT29 + ST = 52ST = 52 – 29ST = 23

Group WorkTell which point is between the

other two1. DE + EF = DF2. BY – OY = BO3. MN – NL = LM

4. RQ = QS – RS5. JH + HI = IJ6. MQ – ML = LQ

E

O

L

R

H

L

ActivityPoint K is between J and M. L is between

K and M. M is between K and N.If JN = 14, KM = 4 and JK = KL = LM,

Find:

1. JK2. LJ3. MJ

4. MN5. KN6. NL

246

81210

Summary

Betweeness refers only to collinear points.

SeatworkThree segment measures are given. The 3 points named are collinear. Determine which point is between the other 2

1. AD = 25ED = 33AE = 58

2. RS = 45TS = 19RT = 26

D

T

G

P

3. GH = 44HK = 87GK = 43

4. PQ = 34QR = 71PR = 37

C5. AB = 32BC = 13.8AC = 18.2

AGREEMENT

Connecting Skills: TransportationOn a train line three towns are

represented by collinear points A, B and C. Town A is 45 miles North of B and C is 10 miles point of A.

Which town is between the other two?