1. D. N. A.
Are the following triangles similar? If yes, state the appropriate triangle similarity theorem. 9 2) 1) 15 12 8
3) Find the value of x and the length of PQ.

2. Parallel Lines and Proportional Parts
Chapter 7-4

3. Use proportional parts of triangles.
Divide a segment into parts.
midsegment
Standard Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Key)
Lesson 4 MI/Vocab

4. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
The converse is true also. B A E D C

5. Example #1 B A E D C 24 26
9.75 9

6. Find the Length of a Side
Lesson 4 Ex1

7. Find the Length of a Side
Substitute the known measures.
Cross products
Multiply.
Divide each side by 8.
Simplify.
Lesson 4 Ex1

8. A. 2.29 B
C. 12 D
Lesson 4 CYP1

9. Find the value of x and y.

10. Determine Parallel Lines
In order to show that we must show that
Lesson 4 Ex2

11. Determine Parallel Lines
Since the sides have proportional length.
Lesson 4 Ex2

12. A. yes
B. no
C. cannot be determined A B C
Lesson 4 CYP2

13. Midsegment Theorem
The midsegment connecting the midpoints of two sides of the triangle is parallel to the third side and is half as long. C E B D A
DE // AB
and
DE = AB

14. Midsegment of a Triangle
Lesson 4 Ex3

15. Midsegment of a Triangle
Use the Midpoint Formula to find the midpoints of
Answer: D (0, 3), E (1, –1)
Lesson 4 Ex3

16. Midsegment of a Triangle
Lesson 4 Ex3

17. Midsegment of a Triangle
If the slopes of
slope of
slope of
Lesson 4 Ex3

18. Midsegment of a Triangle
Lesson 4 Ex3

19. Midsegment of a Triangle
First, use the Distance Formula to find BC and DE.
Lesson 4 Ex3

20. Midsegment of a Triangle
Lesson 4 Ex3

21. A. W (0, 1), Z (1, –3) B. W (0, 2), Z (2, –3) C. W (0, 3), Z (2, –3)
D. W (0, 2), Z (1, –3)
Lesson 4 CYP3

22. A. yes
B. no A B
Lesson 4 CYP3

23. A B
A. yes
B. no
Lesson 4 CYP3

24. Parallel Proportionality TheoremB A F D C E
If 3 // lines intersect two transversals, then they divide the transversals proportionally.

25. Example #2 Find ST SP // TQ // UR Corresponding Angle Thm.9 U T S Q R 15 11
SP // TQ // UR
Corresponding Angle Thm.
Parallel Proportionality Theorem

26. Example #4 Solve for x and y 37.5 – x Solving for x J K M N L 7.5 9
13.5 x y
37.5
What is JL?
37.5 – x

27. Example #4 Solve for x and y Solving for y J K M N L 7.5 9 13.5 x y
37.5
JKL~JMN
AA~Theorem

28. Proportional Segments
MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.
Lesson 4 Ex4

29. Proportional Segments
Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.
Triangle Proportionality Theorem
Cross products
Multiply.
Divide each side by 13.
Answer: 32
Lesson 4 Ex4

30. In the figure, Davis, Broad, and Main Streets are all parallel
In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.
A. 4
B. 5
C. 6
D. 7
Lesson 4 CYP4

31. Subtract 2x from each side.
Congruent Segments
Find x and y.
To find x:
Given
Subtract 2x from each side.
Add 4 to each side.
Lesson 4 Ex5

32. Congruent Segments To find y:
The segments with lengths are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal.
Lesson 4 Ex5

33. Multiply each side by 3 to eliminate the denominator.
Congruent Segments
Equal lengths
Multiply each side by 3 to eliminate the denominator.
Subtract 8y from each side.
Divide each side by 7.
Answer: x = 6; y = 3
Lesson 4 Ex5

34. Find a. A.
B. 1
C. 11
D. 7
Lesson 4 CYP5

35. Find b.
A. 0.5
B. 1.5
C. –6
D. 1
Lesson 4 CYP5

36. Homework
Chapter 7-4
Pg 410
13-21, 26 – 27, 32 – 36, 61