1

Opener:

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

2

Homework Questions:

3

Review:

AB

C

D

E

F

1. Write a similarity ratio for the triangles. What options do you have for proving ~ ?

2. Are the triangles ~? If so, provide a similarity ratio and statement. Find the value of "a" 2 different ways.

W

XY

Z

V

a ‐ 3

16

6

14

9

12

4

Sections 7.4: Applying Properties of Similar Triangles

W

XY

Z

V

12

16

6

16

9

12

We decided that these two triangles were similar by SAS~. What other information could we add to our picture now?

Are there any other equal proportions created by our parallel lines?

Triangle Proportionality Theorem:

5

Example: Find CY. Solve this problem 2 ways. Compare your answers.

Method 1 ‐ Use similar triangles (Review)

Method 2 ‐ Use the Triangle Proportionality Theorem

49

10 A

XB

C Y

6

Example:

Are the sides of the triangle below divided proportionally?

Can we make any additional conclusions about the figure?

K M J

N

L

21 42

15

30

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.

7

What will happen if we have parallels but no triangle?

A B

C D

E F

X

Two‐Transversal Proportionality Corollary

8

2.6 cm

2.4 cm1.4 cm 2.2 cm

Example:

9

Do you see any possible proportions in thise figure?

A

CBD

What about when it's not a right triangle? Do we have an argument for a true proportion?

K M J

L

N

10

Example:

Find RV and VT if SV is an angle bisector.

R

S T

V10

x + 2

14

2x + 1

11

12

1. 2.

3. 4.

13

5. 6.

7. 8.

14

9. 10.

11.

15

12. 13.

14.