Date___________
Day _____
Postulate (axiom): an accepted rule without a given proof.
Ruler Postulate:
The points on a line can be matched one to one with the
real numbers.
The distance between points A and B is the absolute
value of the difference.
No line
over AB
means
distance!
When three points are collinear, you can say that one point is
____________ the other two.
* Between - ____________________________________
Segment Addition Postulate:
If B is between A and C, then ________________.
If AB + BC = AC, then B is ____________, A and C.
“________________________________________________________ ”
Example: Find a length.
Use the diagram to find BC.
Solution
Use the Segment Addition Postulate to write an equation. Then solve the equation to find BC.
AC = AB + BC
___= ___ + BC
___ = BC
Segment Addition Postulate
Substitute 32 for AC and 10 for AB.
Subtract 10 from each side.
1.) Use the diagram to find BC.
(a)
2.)Draw a sketch of the three collinear points,
where X is between Y and Z. Then write the
segment addition postulate for the points.
3.) Suppose K is between L and M. Use the
segment addition postulate to solve for the
variable. Then find the lengths of LK, KM,
and LM.
LK= 7y + 9
KM = 3y + 4
LM = 143
4.) Let J be between R and N. If
RJ = 3x + 16, NJ = 2x – 8, and
NR = 7x – 12. Find the length of the
entire segment.
(b)
Congruent Segments: Line segments that have the same length.
NOTICE!!!
1) Hash marks on
segments
2) Different notation
between length and
congruent
WRITE: Describe the differences between when you use “equal” and
when you use “congruent?” Give a SPECIFIC example of each.
Construct!
Construct a segment GH that is congruent to EF
5.) In the diagram, points P, Q, R and S are collinear. PS = 46, PR = 18, and PQ = QR. Find the indicated
length.
(a) PQ
(b) QR
(c) RS
(d) QS
Midpoint: point that divides a segment into two congruent segments
Definition of Midpoint: If K is the midpoint of MN , then
_____________
Diagram/label:
How do we know if a point is a midpoint?
Compare midpoint to point between:
Segment Bisector: a ray, line, or line segment that intersects the
segment at its midpoint
Definition of Segment Bisector: If line q bisects MN at point P, then
__________
Diagram/label:
Example 1: Find Segment Lengths
In the diagram, line l bisects AC at point B, and AB = 8 in. Find AC.
Solution:
Point B is the midpoint of AC . So, AB = BC = 8 in.
AC = AB + BC
Segment Addition Postulate
= ____ + ____
Substitute 8 for AB and 8 for BC.
= ____ in.
Add.
Exercises:
1.) Find AC if AB = 10 cm.
2.) Point W bisects UV .
Find UV if WV = 14 inches.
3.) Find MF.
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Construct a segment bisector: