4.1 warm-up A triangle is enlarged by a scale factor of 9. If the length of one side of the larger triangle is 202.5 centimeters, what is the length of the corresponding side of the smaller triangle? f. 13.5 cm g. 22.5 cm h. 72 cm j. 202.5 cm 8

5.2 Bisectors in Triangles

You will learn the meaning of an angle bisector and a triangle bisector.

Starting off with Theorems Perpendicular Bisector If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. A B D C

Here is another Theorem Converse of the Perpendicular Bisector If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. D C A B

And another Theorem Angle Bisector If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.. C B A D

Converse of the Angle Bisector Last Theorem Converse of the Angle Bisector If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector. D C B A

Try this one Find x. 2x - 4 = 4x - 16 - 4x - 4x -2x - 4 = - 16 + 4 + 4 C B A 4x-16 D Find x. 2x - 4 = 4x - 16 - 4x - 4x -2x - 4 = - 16 + 4 + 4 -2x = -12 - 2 - 2 x = 6

Try this one Now x=6, find BD. 4x - 16 4*6 - 16 24 - 16 8 2x-4 4x-16 C A 4x-16 D Now x=6, find BD. 4x - 16 4*6 - 16 24 - 16 8

Triangle Midsegment Theorem 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 || 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. A B M P C MP || AB MN || CB NP || AC

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

Here is the assignment.