Bellwork4) Suppose you know PQ and QR. Can you use the segment addition postulate to find PR? Explain.

1-3 Measuring Segments 1-3 Measuring Segments and Anglesand Angles

Postulate 1Postulate 1: Ruler post.: Ruler post.• The points on a line can be The points on a line can be

matched with those on the real # matched with those on the real # line.line.

• The real # that corresponds to a The real # that corresponds to a point is the point is the coordinatecoordinate of the of the

point.point.• If you find the If you find the differencedifference between between

the coordinates of 2 points, then the coordinates of 2 points, then take the take the absolute valueabsolute value, you will , you will have the have the distancedistance between the between the

points.points.

Ruler post.Ruler post. (continued) (continued)

• The length of AB can be found by x2-x1

• **The symbol for the length of AB is AB.

AA BB

xx11 xx22

ExampleExample: Find AB.: Find AB.

AA BB

Point A is at 1.5 and B is at 5.Point A is at 1.5 and B is at 5.

So, AB = 5 - 1.5 = 3.5So, AB = 5 - 1.5 = 3.5

Is Alex Is Alex betweenbetween Ty and Josh? Ty and Josh?

In order for a point to be between 2 others, all 3 points MUST BE collinear!!

TyTy AlexAlex JoshJosh

Yes!Yes!

No, but No, but why not?why not?How about now?How about now?

Post. 1-6Post. 1-6: Segment Addition Post.: Segment Addition Post.

• If B is between A & C, then

AB + BC = AC.

• If AB + BC = AC, then B is between A & C.

AA BBCC

EX.

• If EG= 59, what are EF and FG?

8x-14 4x+1E F G

OYO.

• If EG= 120, what are EF and FG?

4x+6 7x+15E F G

ExEx: if DE=2, EF=5, and : if DE=2, EF=5, and DE=FG, find FG, DF, DG, & DE=FG, find FG, DF, DG, &

EG.EG.

DD EE

FFGG

FG=2FG=2

DF=7DF=7

DG=9DG=9

EG=7EG=7

Congruent ( ) SegmentsCongruent ( ) Segments

• Segments that have the same length.

If AB & XY have the same length,

Then AB=XY,

but

AB XY

Symbol for congruentSymbol for congruent

• Midpoint- a point that divides the segment into two congruent segments

• Segment Bisector- a point, line, or ray that intersects a segment at its midpoint

Ex..

• Q is the midpoint of PR. What are PQ,QR, and PR?

6x-7 5x +1P Q R