Chapter 1: Tools of Geometry

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Presentation transcript:

Chapter 1: Tools of Geometry Lesson 5: Measuring Segments

Definitions Congruent- same shape and size (segments that have the same measure)

Distance between points A. Find LM. B. Find XZ.

Postulate 1-5 Ruler Postulate The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B. AB = I a- b I Use |Absolute Value|!!! A B Since A is at -2 and B is at 4, we can say the distance from A to B or B to A is: -2 – 4 = 6 or 4 – (-2) = 6

Postulate 1-6 Segment Addition Postulate If three points, A, B, and C are collinear and B is between A and C, then AB + BC= AC. 2x 4x + 6 C A B AB = 2x BC = 4x + 6 AC = 60 Use the Segment Addition Postulate find the measure of AB and BC.

Step 1: AB + BC = AC (Segment Addition) 2x + 4x + 6 = 60 6x + 6 = 60 6x = 54 x =9 AB = 2x = 2(9) = 18 BC =4x + 6 = 4(9) + 6 = 42 Step 2: Step 3: Step 4:

Use the diagram to find GH. EXAMPLE 3 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.

Definitions Midpoint- the point on a segment that divides the segment into two congruent segments Segment bisector- any line, segment or plane that intersects a segment at its midpoint

Homework Pg 33 1-15