Transcript 1.2-1.3 Using Segments, Congruence, midpoints and Distance

1.2-1.3 Using Segments,
Congruence, midpoints and Distance
Learn Segment Postulates so you can identify
segment congruence.
Learn midpoint and distance formulas so you
can find measurements in coordinate plane
In the study of geometry, definitions,
postulates and undefined terms are
accepted as true w/o verification or
proof.
These 3 types of statements can be used
to prove that theorems are true.
Proof – logical argument backed by
statements that are accepted as true.
3 types of proofs-paragraph
(informal), 2 column (used most often) and flow
chart
Congruence – means equal. We can say that 2
lines that have the same measure are
“congruent”. We use the symbol 
Ruler Postulate
The pts on any line can be paired with real numbers
so that given any 2 pts P and Q on the line. P
corresponds to zero and Q corresponds to a positive
number.
Segment Addition Postulate
If Q is between P and R, then PQ + QR = PR
If PQ + QR = PR, then Q is between P and R
Using a straight edge and compass
only:
Draw a segment in your notes using a straight edge.
Now, using a straight edge and compass, construct a
segment congruent to the one you drew without
using the markings on the ruler side of your straight
edge.
Explain how you did it 
Using your straight edge and compass, construct a picture
to explain the segment addition postulate and how it
works.
Find LM if L is between N and M, NL
= 6x – 5, LM = 2x + 3 and NM = 30.
Prove each step!
6x - 5
N
L
Hint: Draw a picture
2x + 3
M
30
6x – 5 + 2x + 3 = 30
8x – 2 = 30
8x = 32
x=4
LM = 2(4) + 3
= 11
Segment addition postulate
Substitution
Addition property
Division property
Substitution
Substitution
*Midpoint – point of a segment that
divides the segment into 2 equal parts.
*Segment bisector – is a point, ray, line,
line segment or plane that intersects the
segment at its midpoint.
Point M is the midpoint of VW . Find the
length of VM .
4x-1
V
VM = MW
4x-1 = 3x + 3
x–1=3
x=4
3x+3
M
W
Definition of midpoint
Substitution
Subtraction property
Addition property
Did we answer the question?
Given
VM = 4x – 1
VM = 4(4) – 1 Substitution
VM = 15 units Substitution
To find the midpoint on coordinate plane
Use the midpt formula:
 x1  x2 y1  y2 
m
,

2 
 2
Find the midpt of between (-3,-4) and (5,7)
35
mx 
2
47
my 
2
M = (1,1.5)
To find the coordinates of end pt given
midpt.
Use the midpt formula, but solve for a different variable.
Find Q given RQ if P(4,-1) and R(3,-2).
x1  x2
mx 
2
3  x2
4
2
8  3  x2
y1  y2
my 
2
 2  y2
-1 
2
- 2  2  y2
(5,0)
Find Q given NQ if L(4,-6) and N(8,-9).
8  x2
4
2
 9  y2
-6 
2
8  8  x2
-12  9  y2
(0,-3)
If y is midpt of xz, xy = 2x+11 and
yz=4x-5, find xz
2x + 11 = 4x - 5
16 = 2x
8=x
xy = 2(8) + 11
= 27
xz = 2(27)
= 54
Distance Formula
d
x2  x1    y2  y1 
2
X coordinate from pt # 1
X coordinate from pt # 2
2
Y coordinate from pt # 1
Y coordinate from pt # 2
Commit this to memory…You are going to need it 
Find JK if J(9,-5) and K(-6,12)
Distance formula:
d
 6  92  12  52
d
 152  17 2
d  225 289
d  514
d  22.6units
Pg 12 13 – 26, 28
Pg 19 3-5, 14-16 (show the
properties), 17-19, 24-27,
31-33
(31 problems total for 2 days…doable )