Which point on the graph satisfies the conditions x<3.3 and y>1.5 ?
a. Point P
b. Point Q
c. Point R
d. Point S0 2 4 6 8
0
2
4
6 R(4,5)Q(2,4
)
P(1,1)
S(5,3)
4.1 warm-up
6
5.1 Midsegments of Triangles
Lets look at some formulas first.
Slope:y2-y1
x2-x1
Midpoint:
Distance:
Find the slope given the points{(2,1), (5,-3)}
m = (y2 - y1) (x2 - x1)
m = (-3 -1)(5 -2)
m = -43
Find the slope given the points{(3,5), (-1,4)}
m = (y2 - y1) (x2 - x1)
m = (4 -5)(-1-3)
m = -1- 4
= 14
Two lines are parallel if and only if they have the same slope.Two lines are parallel if and only if they have the same slope.
example:
example:
PardekooperPardekooper
Two lines are perpendicular if and Two lines are perpendicular if and only if their slopes are opposite only if their slopes are opposite inverses.inverses.
(0.45,7) and (-0.3,-9)
Find the midpoint between two points.
(0.075,-1)
(-0.3+ 0.452
, -9 + 72 )
PardekooperPardekooper
(6,6) and (19,6)
(12.5, 6)
( 19+ 62
, 6 + 62 )
PardekooperPardekooper
Find the midpoint between two points.
PardekooperPardekooper
Find the distince between two points.
(6,6) and (19,6)
13
Here comes a theorem !
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then segment is parallel to the third
side, and is half its’ length
A B
C
D E
AB || DEDE=1/2AB
Now, it’s your turn.
Given M, P, and N are midpoints, look at the diagram and name the sets of parallel segments.
A B
C
M P
N
MP || AB
NP || AC
MN || CB
Given MP=5, find AB
A B
C
M P
N
How about some numbers.
5
If MP=1/2AB,
then AB=2*MP
AB=2*5 AB=10
Given CB=25, find MN
25
Remember MM=1/2CB
CB=25
MN=12.5
AssignmentWorkbook
Page 339 all
1a. 8cm
1b. 16cm
1c. 14cm
2a. 22.5in.
2b.15.5in.
2c. 15.5in.
3a. 9.5cm
3b. 17.56cm
3c. 14.5cm
4. 17
5. 20.5
6. 7
7. 6.73cm
8. 42
9. 16.5
10a. 18
10b. 61
11.AB || HI BC || GI
AG || HI BH || GI
GB || HI HC || GI
AC || GH
AI || GH
IC || GH
12. PQ || XZ
PQ ||XR
PQ || RZ
PR || YQ
PR || QZ
PR || YZ
RQ || YX
RQ || YP
RQ || PX