#### Transcript Slide 1

**5-Minute Check on Lesson 6-3**

**Transparency 6-4 Determine if each pairs of triangles are similar. If so, write a similarity 1.**

**statement. Justify your statement.**

**9 D E C 4.5**

**4.8**

**G H 9.0**

**7.6**

**J I 5.7**

**6.75**

**L K 3.6**

**12 A B ∆BAC ~ ∆DEC AA Similarity No. Sides are not proportional ∆GHI ~ ∆KLJ SSS Similarity A -0.8**

**S R 3 V 5 U 8 0.8**

**T C 1.2**

**D 4.8**

**Click the mouse button or press the Space Bar to display the answers.**

**Lesson 6-4**

**Parallel Lines and Proportional Parts**

**Objectives**

•

**Use proportional parts of triangle**

•

**Divide a segment into parts**

**Vocabulary**

•

*Midsegment: *

*Midsegment:*

*a segment whose endpoints are the midpoints of two sides of the triangle*

**Example 1a**

**In ∆RST, RT // VU, SV = 3, VR = 8, and UT = 12. Find SU.**

*S*

From the Triangle Proportionality Theorem, Multiply.

Divide each side by 8.

Simplify.

**Answer:**

**Example 1b**

**In ∆ABC, AC // XY, AX=4, XB=10.5 and CY=6. Find BY.**

*B*

**Answer: 15.75**

**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: **

lengths, since the segments have proportional

**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

**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

**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

**Example 4a**

**Find ***x ***and ***y***.** To find

*x*

: Given Subtract 2

*x*

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 8

*y*

from each side.

Divide each side by 7.

**Answer: **

*x*

= 6;

*y*

= 3

**Find a and b.**

**Example 4b**

**Answer: **

*a*

= 11;

*b*

= 1.5

**Summary & Homework**

•

**Summary:**

–

**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**