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Bellwork. 4) Suppose you know PQ and QR. Can you use the segment addition postulate to find PR? Explain. 1-3 Measuring Segments and Angles. Postulate 1 : Ruler post. The points on a line can be matched with those on the real # line. - PowerPoint PPT Presentation
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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