Transcript Slide 1

5-Minute Check on Lesson 6-1
Transparency 6-2
1. There are 480 sophomores and 520 juniors in a high school. Find
the ratio of juniors to sophomores.
13:12
2. A strip of wood molding that is 33 inches long is cut into two pieces
whose lengths are in the ratio of 7:4. What are their lengths?
21 and 12 inches
Solve each proportion.
3.
6
72
--- = --x
84
4.
39
4x
--- = ---57
19
5.
2x – 1
x+4
-------- = --------4
8
6.
x=7
x = 13/4 = 3.25
x=2
The ratio of the measures of the three angles
of a triangle is 13:6:17. Find the measure of the largest angle. 85
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Lesson 6-2
Similar Polygons
Objectives
• Identify similar figures
• Solve problems involving scale factors
Vocabulary
• Scale factor – the ratio of corresponding
sides of similar polygons
Similar Polygons
R
Congruent Corresponding Angles
A
C
B
mA = mP
mB = mQ
mC = mR
mD = mS
P
S
D
Corresponding Side Scale Equal
AC
AB
CD
DB
---- = ---- = ---- = ---PR
PQ
RS SQ
Q
Example 1a
Determine whether the pair of figures is similar.
Justify your answer.
Q
The vertex angles are marked as 40º and 50º, so they are
not congruent. Since both triangles are isosceles, the
base angles in each triangle are congruent. In the first
triangle, the base angles measure ½ (180 – 40) or 70°
and in the second triangle, the base angles measure ½
(180 – 50) or 65°
Answer: None of the corresponding angles are congruent,
so the triangles are not similar.
Example 1b
Determine whether the pair of figures is similar.
Justify your answer.
T
Since the measures of all the corresponding angles are equal,
then the angles must be congruent.
Answer: The ratio of the measures of the corresponding sides are
equal and the corresponding angles are congruent, so ∆ABC ~ ∆RST
Example 1c
Determine whether the pair of figures is similar.
Justify your answer.
Answer: Only one pair of angles are congruent, so the
triangles are not similar.
Example 2a
An architect prepared a 12-inch model of a skyscraper to look
like a real 1100-foot building. What is the scale factor of the
model compared to the real building?
Before finding the scale factor you must make sure that both
measurements use the same unit of measure.
1100(12) 13,200 inches
Answer: The ratio comparing the two heights is
The scale factor is
which means that the model is
of the real skyscraper.
,
the height
Example 2b
A space shuttle is about 122 feet in length. The Science
Club plans to make a model of the space shuttle with a
length of 24 inches. What is the scale factor of the
model compared to the real space shuttle?
Answer:
Example 3a
The two polygons are similar. Write a similarity
statement. Then find x, y, and UV.
Use the congruent angles to write
the corresponding vertices in order.
To find x:
Similarity proportion
Multiply.
Divide each side by 4.
Example 3a cont
To find y:
Similarity proportion
Cross products
Multiply.
Subtract 6 from each side.
Divide each side by 6 and
simplify.
Answer:
Example 3b
The two polygons are similar. Find the scale factor
of polygon ABCDE to polygon RSTUV.
The scale factor is
the ratio of the
lengths of any two
corresponding sides.
Answer:
Example 3c
The two polygons are similar.
a. Write a similarity statement. Then find a, b, and ZO.
Answer:
;
b. Find the scale factor of polygon TRAP to polygon ZOLD
.
Answer:
Summary & Homework
• Summary:
– In similar polygons, corresponding angles are
congruent, and corresponding sides are in (the
same ratio) proportion
– The ratio of two corresponding sides in two similar
polygons is the scale factor
• Homework:
– pg 293-5: 4, 6, 7, 12, 13, 27-31, 36, 38