1.2 – Use Segments and Congruence

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Presentation transcript:

1.2 – Use Segments and Congruence Geometry Ms. Rinaldi

Postulate 1 – The Ruler Postulate In Geometry, a rule that is accepted without proof is called a postulate or axiom. Postulate 1 – The Ruler Postulate

EXAMPLE 1 Apply the Ruler Postulate Measure the length of ST to the nearest tenth of a centimeter. The length of ST is about 3.4 centimeters. ANSWER

EXAMPLE 2 Apply the Ruler Postulate Use a ruler to measure the length of the segment to the nearest inch. 1 8 a. 1 in. 5 8 ANSWER b. 1 in. 3 8 ANSWER

Definition Between –

Postulate 2 – Segment Addition Postulate

EXAMPLE 3 Apply the the Segment Addition Postulate 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. SOLUTION 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

EXAMPLE 4 Find a length In Exercises 3 and 4, use the diagram shown. a. Use the Segment Addition Postulate to find XZ. 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. b. No; W is not between X and Z. ANSWER

Use the diagram to find GH. EXAMPLE 5 Find a length Use the diagram to find GH. SOLUTION Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. FG + GH = FH Segment Addition Postulate. 21 + GH = 36 Substitute 36 for FH and 21 for FG. = 15 GH Subtract 21 from each side.

EXAMPLE 6 Find a length Use the diagram to find WX. 107 ANSWER

Definition Congruent Segments –

EXAMPLE 7 Compare segments for congruence 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 8 Compare segments for congruence 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.

Homework Pages 12 – 13 # 1, 6-14, 20, 21-23

A. Answer the following. 2. D, E & F are the three collinear points. If DE = FE and DE = 2x + 8, FE = 5x + 2, find x. 6. Given the figure below. SOLUTION: Write an equation for x using definition of congruent segments, then solve. DE = FE ( GIVEN) 2x + 8 = 5x + 2 8 – 2 = 5x – 2x 6 = 3x 2 = x D E F 2x + 8 5x +2