1.2 Key Concepts. Postulate A rule that is accepted without proof. Sometimes called an Axiom.

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Presentation transcript:

1.2 Key Concepts

Postulate A rule that is accepted without proof. Sometimes called an Axiom.

Theorem A AA A rule that can be proved.

Congruent Segments Line Segments that have equal lengths

Ruler Postulate T TT The points on a line can be matched one to one with real numbers. The number that corresponds to a point is the COORDINATE of that point.

T TT The DISTANCE between points is the absolute value of the difference of the coordinates. Example

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

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 = = 740 The distance from Lubbock to St. Louis is about 740 miles. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Use a ruler to measure the length of the segment to the nearest inch

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; W is not between X and Z. ANSWER

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 GH = 36 FG + GH=FH = 15GH

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.

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

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.