Index Card Let’s start our stack of Theorems, Postulates, Formulas, and Properties that you will be able to bring into a quiz or test. Whenever I want.

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1.3 Use Midpoint and Distance Formulas

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Presentation transcript:

Index Card Let’s start our stack of Theorems, Postulates, Formulas, and Properties that you will be able to bring into a quiz or test. Whenever I want you to add to your Theorem or Postulates I will set the background to bright yellow Lesson 1-1 Point, Line, Plane 1

Lesson : Segments and Rays The Segment Addition Postulate If C is between A and B, then AC + CB = AB. The length of a line segment is equal to the sum of its parts. Postulate: Example: If AC = 4, CB = 8 then AB = AC + CB = =

Lesson 1-2: Segments and Rays 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: )

Lesson 1-2: Segments and Rays 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. Formulas:

In a coordinate plane for a line segment whose endpoints have coordinates and. Lesson 1-2: Segments and Rays Midpoint The midpoint is given by:.

In a coordinate plane for a line segment whose endpoints have coordinates and Lesson 1-2: Segments and Rays Midpoint Formula The midpoint is given by:.

Lesson 1-2 Practice Find the midpoint between (7, -2) and (-4, 8).

Lesson 1-2: Segments and Rays Segment Bisector Any segment, line or plane that divides a segment into two congruent parts is called segment bisector. Definition:

The Distance Formula 9

10

Lesson 1-2 The Distance Formula The distance d between any two points with coordinates and is given by the formula d =.

Lesson 1-2 The Distance Formula Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2, y 2 = 1 d = Example:

Lesson 1-2: Formulas Practice Find the distance between (3, 2) and (-1, 6).

Lesson 1-2: Formulas Homework Pg. 19 # 8, 12, 16, 19, 21 Pg 20 # 24, 26, 32 Pg 21 # 52