1.2 Use segments and Congruence You will use segment postulates to identify congruent segments....
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1.2 Use segments and Congruence You will use segment postulates to identify congruent segments. Essential Question: What are congruent segments?
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Transcript of 1.2 Use segments and Congruence You will use segment postulates to identify congruent segments....
1.2 Use segments and Congruence
You will use segment postulates to identify congruent segments.
Essential Question: What are congruent segments?
Warm-Up ExercisesEXAMPLE 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 ExercisesEXAMPLE 2 Apply the the Segment Addition Postulate
SOLUTION
MapsThe 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 ExercisesGUIDED 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.58
ANSWER
1 in.38
ANSWER
Warm-Up ExercisesGUIDED 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 ExercisesEXAMPLE 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 ExercisesEXAMPLE 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 ExercisesEXAMPLE 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 ExercisesGUIDED PRACTICE for Examples 3 and 4
5. Use the diagram to find WX.
107ANSWER
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 ExercisesDaily Homework Quiz
1. Measure AB to the nearest inch.18
2. Find CE.
ANSWER 22
ANSWER 381
Warm-Up ExercisesDaily 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.
1.2 Use segments and Congruence
You will use segment postulates to identify congruent segments.
Essential Question: What are congruent segments?
To find the distance between two points on a number line, subtract their coordinates and find the absolute value of the difference.The length of a segment is the sum of the lengths of its nonoverlapping parts.
Congruent segments are segments that have the same length.
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