Which point on the graph satisfies the conditions x<3.3 and y>1.5 ? Point P Point Q Point R

4.1 warm-up 6 R(4,5) Q(2,4) Which point on the graph satisfies the conditions x<3.3 and y>1.5 ? Point P Point Q Point R Point S 4 S(5,3) 2 P(1,1) 0 0 2 4 6 8 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 = -4 3

Find the slope given the points{(3,5), (-1,4)} m = (y2 - y1) (x2 - x1) m = (4 -5) (-1 -3) m = -1 = 1 - 4 4

Two lines are parallel if and only if they have the same slope. example: Two lines are perpendicular if and only if their slopes are opposite inverses. example: Pardekooper

Find the midpoint between two points. (0.45,7) and (-0.3,-9) ( ) -0.3 + 0.45 + 7 -9 , 2 2 (0.075,-1) Pardekooper

Find the midpoint between two points. (6,6) and (19,6) ( ) 19 + 6 6 + 6 , 2 2 (12.5, 6) Pardekooper

Find the distince between two points. (6,6) and (19,6) 13 Pardekooper

Here comes a theorem ! A B D E C 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 AB || DE DE=1/2AB

Now, it’s your turn. N Given M, P, and N are midpoints, look at the diagram and name the sets of parallel segments. B A P M C MP || AB MN || CB NP || AC

How about some numbers. If MP=1/2AB, then AB=2*MP MN=12.5 CB=25 AB=2*5 AB=10 Remember MM=1/2CB N A B P M 5 25 C Given MP=5, find AB Given CB=25, find MN

Assignment Workbook Page 339 all

6. 7 7. 6.73cm 8. 42 9. 16.5 10a. 18 10b. 61 AB || HI BC || GI AG || HI BH || GI GB || HI HC || GI AC || GH AI || GH IC || GH 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 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 x<3.3 and y>1.5 ? Point P Point Q Point R