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Lesson 1-1 Point, Line, Plane 1
Index Card
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Lesson : Segments and Rays
The Segment Addition Postulate
AB
C
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
= 4 + 8
= 12
84
12
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 )
AB
D
C
Congruent segments can be marked with dashes.
Correct notation:
Incorrect notation:
AB = CD AB CD
AB = CDAB CD
Segments with equal lengths. (congruent symbol: )
Lesson 1-2: Segments and Rays
Midpoint
a b
2
A point that divides a segment into two congruent segments
Definition:
EDFIf DE EF , then E is the midpoint of DF.
On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is .
Formulas:
Lesson 1-2: Segments and Rays
In a coordinate plane for a line segment whose endpoints have coordinates and
.
Midpoint
1 1( , )x y 2 2( , )x y
1 2 1 2,2 2
x x y yThe midpoint is given by:
.
Lesson 1-2: Segments and Rays
In a coordinate plane for a line segment whose endpoints have coordinates and
Midpoint Formula
1 1( , )x y 2 2( , )x y
1 2 1 2,2 2
x x y yThe midpoint is given by:
.
Lesson 1-2
Practice
Find the midpoint between (7, -2) and (-4, 8).
Lesson 1-2: Segments and Rays
Segment BisectorAny segment, line or plane that divides a segment into two congruent parts is called segment bisector.
Definition:
B
E
D
FA
BE
D
FA
E
D
A F
B
AB bisects DF. AB bisects DF.
AB bisects DF.Plane M bisects DF.
The Distance Formula
9
The Distance Formula
10
Lesson 1-2
The Distance Formula
1 1( , )x yThe distance d between any two points with coordinates and is given by the formula d = .2 2( , )x y 2 2
2 1 2 1( ) ( )x x y y
Lesson 1-2
The Distance Formula
Find the distance between (-3, 2) and (4, 1)
x1 = -3, x2 = 4, y1 = 2 , y2 = 1
( 3 4)2 (2 1)2d =
( 7)2 (1)2 49 1d =
50 or 5 2 or 7.07d =
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