1.3 Segments and Their Measures

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Presentation transcript:

1.3 Segments and Their Measures Objectives: Use the Segment Addition Postulate. Use the Distance Formula to find the distance between two points.

Basic Vocabulary Postulate Theorem a rule that is accepted as true without proof Theorem a rule that must be proven true.

Postulates Ruler Postulate AB = | x2 – x1 | names of the points A B x1 coordinates of the points AB = | x2 – x1 | The distance between points A and B or the length of AB

This indicates that the points are collinear. Postulates Segment Addition Postulate If B is between A and C then AB + BC = AC A B C This indicates that the points are collinear.

add up to the whole segment. Postulates Segment Addition Postulate If B is between A and C then AB + BC = AC A B C AB BC AC The pieces of a segment add up to the whole segment.

The postulate also works in reverse Postulates Segment Addition Postulate If A, B , and C are collinear and AB + BC = AC then B is between A and C A B C AB BC AC The postulate also works in reverse

Example 1: E D F

Example 2: x E x 9 D 35 C B A

Practice 1: x 2x D 2 C 20 B A

Example 3: Find the distance between Sue’s house and Jane’s house. 425 yds 267 yds 425 + 267 692 yds

Example 4: A truck with a trailer has a total length of 27 feet. If the trailer has a length of 15 feet, how long is the truck? 12 feet 15 feet 27 – 15 27 feet

Theorem The Distance Formula If A(x1, y1) and B(x2, y2) are points on a coordinate plane then the distance between A and B is x y A B C

Definition Congruent Segments segments that have the same length B Y A X the symbol for congruent this represents a number equal to a number this represents a figure the same size and shape as another figure

Example 5: Find the lengths of the segments. Are any of the segments congruent? x y

Example 5: Find the lengths of the segments. Are any of the segments congruent? x y

none of the segments are congruent Example 5: none of the segments are congruent Find the lengths of the segments. Are any of the segments congruent? x y

Practice 3: Find the distance between the points. A (3, 1) B (0, 4)

Summary What is a postulate? Describe how to use the Distance Formula Describe how to use the Segment Addition Postulate. Describe how to use the Distance Formula