1. Warm-Up #26

2. homework
Lesson 2: Triangle Side Splitter
Front side

3. Side-Splitter Theorem

4. Side-Splitter Theorem
Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. OR

5. Side-Splitter Proof
Statements
Reasons 1. 2. 3. 4. 5. 6. 7.

6. Proof: http://mathbitsnotebook.com/Geometry/Similarity/SMSplitter.html

7. Side-Splitter Theorem
Find the value of x.
Find the value of x.

8. Corollary to Side-Splitter Theorem
Corollary to Theorem 7-4: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

9. Application
Given that the edges of the panels of the sails are parallel, find the values of the variables.

10. You wanna try one? Too bad! ;)
Find the values of the variables in the following figure.

11. Homework
Relationship of Triangles

12. Relationship of Similar Triangles

13. Triangle-Angle-Bisector Theorem
Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

14. Triangle-Angle-Bisector Theorem
Find the value of x in the following figure.
Find the value of x in the following figure.

15. Kick it up a notch!!!
Find the value of x.

16. Kick it up a notch!!!
Find the value of x.

17. Midsegments of Triangles
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half of its length
Midsegment = ½ of Base
Midsegment x 2x

18. Find the length of the midsegment.
M = ½ b 23
M = ½ • 46 46
M = 23

19. Find the length of the base.
M = ½ b 46 2•
46= ½ b 2• 92
92 = b

20. Find the length of the midsegment and the base.
5•3-1
= 14
M = ½ b
5x - 1
5x - 1 = ½(6x + 10)
5x - 1 = 3x + 5
6x + 10
-3x x
2x - 1 = 5
6•3+10
= 28
+1 +1
2x = 6
x = 3

21. Midsegments of Triangles
In ΔEFG, H, J, and K are midpoints. Find HJ, JK, and FG. F
HJ:
JK:
FG: 60 H J 40 G E K
100

22. Midsegments of Triangles
AB = 10 and CD = 18. Find EB, BC, and AC A B E D C
EB:
BC:
AC:

23. Midsegments
Find m<VUZ. Justify your answer.
65° X Y V Z U

24. In the diagram, ST and TU are midsegments of triangle PQR
In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU.
5 ft
16 ft
TU = ________
PR = ________

25. In the diagram, XZ and ZY are midsegments of triangle LMN
In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY.
14 cm
53 cm
ZY = ________
MN = ________