1 Lesson 1-3 Measuring Segments

2 Postulates: An assumption that needs no explanation. Postulate 1-1 Through any two points there is exactly one line. Through any three noncollinear points, there is exactly one plane. Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one point. P m n If two distinct planes intersect, then they intersect in exactly one line. Postulate 1-3 Postulate 1-4 A B P

3 The Ruler Postulate The Ruler Postulate (Postulate 1-5): Every point on a line can be paired with a real number. This makes a one to one correspondence between the points on the line and the real numbers. The real numbers that corresponds to a point is called coordinate of the point. The distance between any two points on a number line is the absolute value of the difference of the real numbers corresponding to the points. Formula: Take the absolute value of the difference of the two coordinates a and b: │a – b │

4 Ruler Postulate : Example PK =| | = 5 Remember : Distance is always positive Find the distance between P and K. Note: The coordinates are the numbers on the ruler or number line! The capital letters are the names of the points. Therefore, the coordinates of points P and K are 3 and -2 respectively. Substituting the coordinates in the formula │a – b │

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6 The Segment Addition Postulate If C is between A and B, then AC + CB = AB. Postulate 1-6: Example: If AC = x, CB = 2x and AB = 12, then, find x, AC and CB. AC + CB = AB x + 2x = 12 3x = 12 x = 4 2x x 12 x = 4 AC = 4 CB = 8 Step 1: Draw a figure Step 2: Label fig. with given info. Step 3: Write an equation Step 4: Solve and find all the answers

7 Congruent Segments Definition: If numbers are equal the objects are congruent. AB: the segment AB ( an object ) AB: the distance from A to B ( a number ) Congruent segments can be marked with dashes. Correct notation: Incorrect notation: Segments with equal lengths. (congruent symbol: )

8 Midpoint A point that divides a segment into two congruent segments Definition: On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is. In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and is. Formulas:

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10 Midpoint on Number Line - Example Find the coordinate of the midpoint of the segment PK. Now find the midpoint on the number line.

11 Segment Bisector Any segment, line or plane that divides a segment into two congruent parts is called segment bisector. Definition: