1. 8.6 Proportions & Similar Triangles
Unit IIA Day 9

2. Do Now
Solve each proportion.
X= 4/3
Z = 49.5
Y= 1.4
Q = 2.5

3. Discovery…

4. Thm. 8.4 Triangle Proportionality Thm.
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
If TU || QS, then _________
RT/TQ = RU/US

5. Thm. 8.5: Triangle Proportionality Converse
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
If RT/TQ = RU/US, then __________
TU || QS

6. Ex. 1: Finding the length of a segment
In the diagram AB || ED, BD = 8, DC = 4, and AE = 12. What is the length of EC?
DC/BD = EC/AE – triangle proportionality thm.
4/8 = EC/12 – substitute
48 = 8EC – Cross multiply
EC = 6

7. Ex. 1A
In the diagram UY is parallel to VX, UV=3 , UW=18, and XW=16. What is the length of YX?
3.2

8. Ex. 2: Determining Parallels
Given the diagram, determine whether MN || GH.
LM/MG = 56/21 = 8/3
LN/NH = 48/16 = 3/1
8/3 ≠ 3/1
MN is not parallel to GH.

9. Ex. 2A Given the diagram, determine whether PQ is parallel to TR.
Yes (3/8)

10. Thm. 8.6
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
If r || s || t and l and m intersect them, then ___________
UW/ WY = VX/ XZ

11. Ex. 3: Using Proportionality Theorems
In the diagram 1  2  3, and PQ = 9, QR = 15, and ST = 11.
What is the length of TU?
Because corresponding angles are congruent, the lines are parallel and you can use Theorem 8.6
PQ/QR = ST/TU -- Parallel lines divide transversals proportionally.
9/15 = 11/TU – Substitute
9TU = 15*11 – Cross multiply
TU = (15*11)/9 = 55/3 = 18 1/3

12. Ex. 3A
In the diagram, 1  2  3, AB = 6, BC = 9, EF = 8. What is x?
16/3

13. Closure
Explain what you know about a triangle cut by a segment that’s parallel to one of its sides.