Which point on the graph satisfies the conditions x 1.5 ? a.Point P b.Point Q c.Point R d.Point S 0 2 4 6 8 0 2 4 6 R(4,5) Q(2,4) P(1,1) S(5,3) 4.1 warm-up.

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Presentation transcript:

Which point on the graph satisfies the conditions x 1.5 ? a.Point P b.Point Q c.Point R d.Point S 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: y 2 -y 1 x 2 -x 1 Midpoint: Distance:

Find the slope given the points {(2,1), (5,-3)} m = (y 2 - y 1 ) (x 2 - x 1 ) m = (-3-1) (5-2) m = -4 3

Find the slope given the points {(3,5), (-1,4)} m = (y 2 - y 1 ) (x 2 - x 1 ) m = (4-5) (-1-3) m = = 1 4

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

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

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

Pardekooper 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 AB C DE AB || DE DE= 1 / 2 AB

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

Assignment Workbook Page 339 all

1a. 8cm 1b. 16cm 1c. 14cm 2a. 22.5in. 2b.15.5in. 2c. 15.5in. 3a. 9.5cm 3b cm 3c. 14.5cm cm a b 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