1.3 Segments & Their Measures.

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Presentation transcript:

1.3 Segments & Their Measures

1.3 Definitions: Postulates Postulates are rules that are accepted without proof. Postulates are also called axioms. Coordinate A coordinate is a real number that corresponds to a point on a line. Distance The distance between two points on a line is the absolute value of the difference between the coordinates of the points. Length The length of a segment is the distance between the endpoints. Between When three points lie on a line, you can say that one of them is between the other two. Distance Formula The Distance Formula is a formula for finding the distance between two points in a coordinate plane. Congruent segments Congruent segments are segments that have the same length.

Postulates Postulates are facts about geometry that are accepted as true.

Ruler Postulate Do not copy all of this Every point on a line can be matched with a coordinate on the number line. The distance between two points is the absolute value of the difference of the coordinates. P Q

Ruler Postulate (in other words) If P is at 15 and Q is at 18, the distance from P to Q is 3. 15 18 P Q The distance from P to Q is written: PQ How is this different from PQ?

Ex. 1 Use the number line to find each measure. 1 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5 6 7 8 9 B D E F H I a) DH b) EI c) FB

Segment Addition Postulate If B is between A and C, then AB + BC = AC. A B C + = A B B C A C

Example 2 Points X, Y, and Z are collinear. If XY = 12, YZ = 47, and XZ = 35, determine which point is between the other two. X Z 35 X Y 12 Y Z 47

Example 3 If QS = 29 and QT = 52, find ST. QS + ST = QT 29 + ST = 52 R S T Q QS + ST = QT 29 + ST = 52 ST = 23

Example 4 If FG = 12 and FJ = 47, find GJ. FG + GJ = FJ 12 + GJ = 47 H J G FG + GJ = FJ 12 + GJ = 47 GJ = 35

If A(x1, y1) and B(x2, y2) are points on the coordinate plane, then: The Distance Formula If A(x1, y1) and B(x2, y2) are points on the coordinate plane, then:

5. Find the distance between the points. Round to the nearest tenth.

6. Find the distance between the points. Round to the nearest tenth. 3.6

7. Find the distance between the points. Round to the nearest tenth. 5.4

Two segments are congruent if and only if they have the same length. Congruent Segments Two segments are congruent if and only if they have the same length. A B X Y

Let’s Practice Pg. 21 ***Show Work*** # 2 - 36 even (omit 14, 16, 18) Begin Now 