Download 1.2 Using Segments and Congruence Notes

1.2 Using Segments and Congruence Notes
1.2 Use Segments and Congruence
Ruler Postulate
Points on a line can be matched one to one with the real numbers called coordinates.
Distance between two points: Always Positive.
Postulate/Axiom: A rule that is ACCEPTED WITHOUT proof
Theorem: A rule that CAN BE proved using definitions, postulates, axioms, corollaries and other theorem.
What is the difference in these two pictures?
#1
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
S U N
#2
R A Y
Congruent segments: segments with equal length.
The length of is equal to the length of OR
is congruent to 1
1.2 Using Segments and Congruence Notes
Ex 2
Segment addition postulate: B is between AC.
AB = 2
AC = 7 Find BC =
Ex 3
Midpoint: Point which divides a segment into 2 congruent parts.
C is the midpoint of AB.
AC = 3x + 5 CB = 2x + 13
x=
AB=
Ex 5
B is THE MIDPOINT OF AC.
AB = x+3
CB = x+5
AC=2x+2
x=
BC=
x=8
answer
AB=58
Ex 4
B is between AC
AC = 23
AB = x+1
BC= 3x­2
x=
BC=
x=6
answer
BC=16
B is the midpoint of AC.
AB = 4x ­1
AC = 10x­20
x=
AB=
can create a two column proof as you solve
x=9
answer
AB=35
Segment Addition and Midpoint Worksheet.docx
x=18
answer
BC=23
Boardwork
You try and we will share as a jigsaw in class.
1. O is between segment DG
DO=3x OG=4x+1 DG=36 x=____ OG=_____
2. A is the midpoint of segment JC
JA=5x+3 AC=3x+11 x=_____ JC=_____
3. O is the midpoint of segment BY
BO= 3x+16 BY=14x­4 x=_____ BY=______
4. A is the midpoint of segment CT
CA= x+2 AT=3x+5 CT=7x­8 x=____ CT=____
2
Attachments
Segment Addition and Midpoint Worksheet.docx