1. The document provides homework questions on similarity and proportionality of triangles, including writing similarity ratios, determining if triangles are similar, using the Triangle Proportionality Theorem, and applying properties of similar triangles. 2. Examples are given to find missing side lengths of triangles using similar triangles or proportionality, as well as determining if sides of triangles are divided proportionally. 3. A two-column proof is outlined to show two lines are parallel based on proportional side lengths, and corollaries on proportionality with parallels and two transversals are discussed.

1. Opener:
Choose one of the homework problems listed on the whiteboard and write up your solution.
Write your name under your work.
1

2. Homework Questions:
2

3. Review:
1. Write a similarity ratio for the triangles. 2. Are the triangles ~?
What options do you have for proving ~ ? If so, provide a similarity ratio
F and statement.
Find the value of "a" 2 different ways.
C V
D 9 a‐3
A
B
Z W
6
E
12 16
14
Y X
3

4. Sections 7.4: Applying Properties of Similar Triangles
We decided that these two triangles were similar by SAS~.
What other information could we add to our picture now?
V
Are there any other equal
9 proportions created by our parallel
12 lines?
Z W Triangle Proportionality Theorem:
6
12 16
16
Y X
4

5. Example: Find CY. Solve this problem 2 ways. Compare your answers.
Method 1 ‐ Use similar triangles (Review)
B 4
X
9
C A
Y 10
Method 2 ‐ Use the Triangle Proportionality Theorem
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6. Example:
Are the sides of the triangle below divided proportionally?
Can we make any additional conclusions about the figure?
21 M 42
K J
30
N
15
L
In your notes, work with your partners to write a 2‐column proof showing MN || KL.
Start with these three steps.
_______________________________________________________________________
1. JM = JN 1. Given
MK NL
2. JM = JN 2. Proportion Property (Plug numbers in the
JM + MK JN + NL Statement to make sure you believe it.)
3. JM = JN 3. (You fill this in.)
JK JL
4. 4.
5. 5.
6. 6.
7. 7.
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7. What will happen if we have parallels but no triangle?
A B
C D
X
E F
Two‐Transversal Proportionality Corollary
7

8. Example:
2.4 cm
1.4 cm 2.2 cm
2.6 cm
8

9. Do you see any possible proportions in thise figure?
A
B C
D
What about when it's not a right triangle? Do we have an argument for a true proportion?
M
K J
L
N
9

10. Example:
R
x+2
Find RV and VT if SV is an angle bisector.
10 V
2x + 1
S T
14
10

11. 11

12. 1. 2.
3. 4.
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13. 5. 6.
7. 8.
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14. 9. 10.
11.
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15. 12. 13.
14.
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