1.2 use segments and congruence

1.21.2 Use Segments and CongruenceBell Thinger1. Solve 3x + 5 + 2x – 4 = 36.

ANSWER 7

2. Find three cities on this map that appear to be collinear.

Chicago, Bloomington, SpringfieldANSWER

1.2

1.2

1.2Example 1

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

1.2

1.2Example 2

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

1.2Guided Practice

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; W is not between X and Z.ANSWER

1.2Example 3

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

1.2

1.2Example 4

SOLUTION

To find the length of a horizontal segment, find the absolute value of the difference of the x-coordinates of the endpoints.

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.

Use Ruler Postulate.JK = 2 – (– 3) = 5

1.2Example 4

SOLUTION

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.

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

1.2Guided Practice

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.

1.2Exit Slip

2. Find CE.

ANSWER 22

1 in.ANSWER 83

1. Measure AB to the nearest inch.81

1.2Exit Slip

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

Homework

Pg 12-14#14, 17, 32, 33, 35