1.2 Notes
1.2 Use Segments and Congruence
Postulate( axiom)
Theorem
POSTULATE 1: RULER POSTULATE
The points on a line can be matched one to one with real numbers. The real number
that corresponds to a point is the _________________ of the point.
The _______________ between points A and B , written AB , is the absolute
value of the difference of the coordinates of A and B .
Apply the Ruler Postulate:
1. Measure the length of CD to the nearest tenth of a centimeter.
Between
Investigation:
Given that N is a point between endpoints M and P of line segment MP , describe how to determine the
length of MP , without measuring, if you are given the lengths of MN and NP .
POSTULATE 2: SEGMENT ADDITION POSTULATE
If B is between A and C , then AB  BC  AC .
If AB  BC  AC , then B is between A and C .
Apply the Segment Addition Postulate:
2. Find QS and PQ .
3. If point B is between A and C . Find AB and BC if AB = 2 x  2, BC = 3 x  4, and AC = 42 .
4. If point P is between L and A . Find LA if PL  x  4, PA  2 x  1, and LA  5 x  3 .
Congruent segments
Compare segments for congruence:
5. Plot F  4,5 , G  –1,5  , H  3,3 , and J (3, –2) in a coordinate plane. Then
determine whether FG and HJ are congruent. Justify with mathematical
reasoning.
6. Use the number line to solve each question.
a. What is KL ?
b. If point R is located at the coordinate 3. Are KR and RL congruent segments? Explain.
c. Point C lies between points K and L . The distance between points K and C is
1
of KL ? What is the
3
coordinate of point C ?
d. Point N lies between points C and L . The distance between points C and N is
coordinate of point N ?
3
of CL ? What is the
4