1. 5-Minute Check on Lesson 6-3
Transparency 6-4
5-Minute Check on Lesson 6-3
Determine if each pairs of triangles are similar. If so, write a similarity statement. Justify your statement.
In the figure below, if RS // VT, then find y.
9.0
6.75
4.8
7.6
3.6
5.7 K L J G H I
4.5 12 9
3.5 A B C D E
∆BAC ~ ∆DEC AA Similarity
No. Sides are not proportional
∆GHI ~ ∆KLJ
SSS Similarity
Standardized Test Practice: R S V U T 5 3 8
y + 12 A
-0.8 B B
0.8 C
1.2 D
4.8
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2. Parallel Lines and Proportional Parts
Lesson 6-4
Parallel Lines and Proportional Parts

3. Objectives Use proportional parts of triangle
Divide a segment into parts

4. Vocabulary
Midsegment: a segment whose endpoints are the midpoints of two sides of the triangle

5. Example 1a S In ∆RST, RT // VU, SV = 3, VR = 8, and UT = 12. Find SU.
From the Triangle Proportionality Theorem,
Multiply.
Divide each side by 8.
Simplify.
Answer:

6. Example 1b B In ∆ABC, AC // XY, AX=4, XB=10.5 and CY=6. Find BY.
Answer:

7. Example 2a
In ∆DEF, DH=18, HE=36, and 2DG = GF. Determine whether GH // FE. Explain.
In order to show that we must show that
Since the sides have proportional length.
Answer: since the segments have proportional lengths,

8. Example 2b
In ∆WXZ, XY=15, YZ=25, WA=18 and AZ=32. Determine whether WX // AY. Explain. X
Answer: No; the segments are not in proportion since

9. Example 3
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.
Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.
Triangle Proportionality Theorem
Multiply.
Divide each side by 13.
Answer: 32

10. Example 3b
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.
Answer: 5

11. Example 4a Find x and y. To find x: Given Subtract 2x from each side.
Add 4 to each side.
To find y: The segments with lengths 5y and (8/3)y + 7 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal.
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

12. Example 4b
Find a and b.
Answer: a = 11; b = 1.5

13. Summary & Homework Summary: Homework:
A segment that intersects two sides of a triangle and is parallel to the third side divides the two intersected sides in proportion
If two lines divide two segments in proportion, then the lines are parallel
Homework:
Day 1: pg 311-2: 9,10, 14-18
Day 2: pg 312-3: 11, 12, 20, 21, 23-26, 33, 34