1. 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 centimeters, what is the length of the corresponding side of the smaller triangle?
f cm g cm
h. 72 cm j cm 8

2. 5.2
Bisectors in
Triangles

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

4. 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

5. 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

6. 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

7. 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

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

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

10. 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

11. 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

12. How about some numbers. Given MP=5, find AB AB=2*5 AB=10If
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

13. Here is the assignment.