Which point on the graph satisfies the conditions x1.5 ? Point P Point Q Point R

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 )


(6,6) and (19,6)

(12.5, 6)

( 19+ 62

, 6 + 62 )


Find the midpoint between two points.


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

Which point on the graph satisfies the conditions x1.5 ? Point P Point Q Point R

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