1. Solve 3x + 5 + 2x – 4 = 36.
ANSWER
7
2. Find three cities on this map that appear to be collinear.
Chicago, Bloomington, Springfield
ANSWER
Warm-Up Exercises
EXAMPLE 1
Apply the Ruler Postulate
Measure the length of ST to the nearest tenth of a centimeter.
SOLUTION
Align one mark of a metric ruler with S. Then estimate the coordinate of T. For example, if you align S with 2, T appears to align with 5.4.
Use Ruler Postulate.
ST = 5.4 – 2 = 3.4
The length of ST is about 3.4 centimeters.
ANSWER
Warm-Up Exercises
EXAMPLE 2
Apply the the Segment Addition Postulate
SOLUTION
Maps
The cities shown on the map lie approximately in a straight line. Use the given distances to find the distance from Lubbock, Texas, to St. Louis, Missouri.
Because Tulsa, Oklahoma, lies between Lubbock and St. Louis, you can apply the Segment Addition Postulate.
LS = LT + TS = 380 + 360 = 740
The distance from Lubbock to St. Louis is �about 740 miles.
ANSWER
Warm-Up Exercises
GUIDED PRACTICE
for Examples 1 and 2
Use a ruler to measure the length of the segment to the nearest inch.
1
8
1.
2.
1 in.
5
8
ANSWER
1 in.
3
8
ANSWER
Warm-Up Exercises
GUIDED PRACTICE
for Examples 1 and 2
3.
Use the Segment Addition Postulate to find XZ.
In Exercises 3 and 4, use the diagram shown.
ANSWER
73
In the diagram, WY = 30. Can you use the Segment Addition Postulate to find the distance between points W and Z? Explain your reasoning.
4.
No; Y is not between W and Z.
ANSWER
Warm-Up Exercises
EXAMPLE 3
Find a length
Use the diagram to find GH.
Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH.
SOLUTION
Segment Addition Postulate.
Substitute 36 for FH and 21 for FG.
Subtract 21 from each side.
21 + GH
=
36
FG + GH
=
FH
=
15
GH
Warm-Up Exercises
EXAMPLE 4
Compare segments for congruence
SOLUTION
To find the length of a horizontal segment, find the absolute �value of the difference of the �x-coordinates of the endpoints.
Use Ruler Postulate.
JK = 2 – (– 3) = 5
Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate plane. Then determine whether JK and LM are congruent.
Warm-Up Exercises
EXAMPLE 4
Compare segments for congruence
To find the length of a vertical segment, find the absolute value of the difference of the y-coordinates of the endpoints.
Use Ruler Postulate.
LM = – 2 – 3 = 5
JK and LM have the same length. So, JK LM.
=
~
ANSWER
Warm-Up Exercises
GUIDED PRACTICE
for Examples 3 and 4
5.
Use the diagram to find WX.
107
ANSWER
No.
ANSWER
Plot the points A(– 2, 4), B(3, 4), C(0, 2), and D(0, – 2) in a coordinate plane. Then determine whether AB and CD are congruent.
6.
Warm-Up Exercises
Daily Homework Quiz
1. Measure AB to the nearest inch.
1
8
2. Find CE.
ANSWER
22
ANSWER
3
8
1
Warm-Up Exercises
Daily Homework Quiz
ANSWER
No, FG = 5 and HJ = 4
4. Find KL
ANSWER
7
3. Plot the points F(–3, 5), G(2, 5), H(3, 1), J(3, –3) in a coordinate plane. Are FG and HJ congruent? Explain.
Warm-Up Exercises