Download 1 - Mira Costa High School

1.2 Use Segments and Congruence
Goal • Use segment postulates to identify congruent segments.
Your Notes
VOCABULARY
Postulate, axiom
A rule that is accepted without proof
Theorem
A rule that can be proved
Coordinate
The real number that corresponds to a point
Distance
The distance between two points A and B, written as AB, is the absolute value of the
difference of the coordinates of A and B.
Between
When three points are collinear, you can say that one point is between the other two.
Congruent segments
Line segments that have the same length
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 _coordinate_ of the point.
The _distance_ between points A and B, written as AB, is the absolute value of the
difference of the coordinates of A and B.
Your Notes
Example 1
Apply the Ruler Postulate
Measure the length of CD to the nearest tenth of a centimeter.
Solution
Align one mark of a metric ruler with C. Then estimate the coordinate of D. For example
, if you align C with 1, D appears to align with _4.7_.
CD = | _4.7_ – _1_ | = _3.7_ Ruler postulate
The length of CD is about _3.7_ centimeters.
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.
Example 2
Apply the Segment Addition Postulate
Road Trip The locations shown lie in a straight line. Find the distance from the starting
point to the destination.
Solution
The rest area lies between the starting point and the destination, so you can apply the
Segment Addition Postulate.
SD = _SR_ + _RD_
Segment Addition Postulate
= _64_ + _87_
Substitute for _SR_ and _RD_.
= _151_
Add.
The distance from the starting point to the destination is _151_ miles.
Your Notes
Example 3
Find a length
Use the diagram to find KL.
Use the Segment Addition Postulate to write an equation. Then solve the equation to find
KL.
_JL_ = _JK_ + KL
Segment Addition Postulate
_38_ = _15_ + KL
Substitute for _JL_ and _JK_.
_23_ = KL
Subtract _15_ from each side.
Example 4
Compare segments for congruence
Plot F(4, 5), G(–l, 5), H(3, 3), and J(3, –2) in a coordinate plane. Then determine
whether FG and HJ are congruent.
Horizontal segment: Subtract the _x-coordinates_ of the endpoints.
FG = | _4 – (–1)_ | = _5_
Vertical segment: Subtract the _Y-coordinates_ of the endpoints.
HJ = | _3 – (–2)_ | = _5_
FG and HJ have the _same_ length. So FG __ HJ .
Checkpoint Complete the following exercises.
1. Find the length of AB to the nearest
1
1
inch.
8
7
inches
8
2. Find QS and PQ.
61; 24
3. Consider the points A(–2, –1), B(4, –1), 0(3, 0), and D(3, 5). Are AB and CD
congruent?
No
Homework
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