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:
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