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

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

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

### 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.

### Example 1b

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

B

### 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.

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

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.

5

### Example 4a

Find x and y. To find

x

: Given Subtract 2

x

from 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.

x

= 6;

y

= 3

Find a and b.

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