Bellwork 4) Suppose you know PQ and QR. Can you use the segment addition postulate to find PR?...

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