Download Essential Objectives: At the completion of this lesson, you should be

Geometry 300
7-3 Similar Polygons
Name__________________
Date___________________
Let’s recall the definition of congruent polygons…
Two polygons are congruent iff all pairs of corresponding sides are _______________________ and all pairs of
corresponding angles are _______________________.
 In other words, congruent polygons have the exact same size and shape.
Key Concepts
We have another term to describe two polygons that have the same shape, but differ in size. We say such
polygons are similar.
Definition of Similar Polygons:
 Two polygons are similar if and only if their corresponding angles are congruent and the measures of
their corresponding sides are proportional.
The symbol for similar is:
The Scale Factor is the ratio of the lengths of two corresponding sides of two similar polygons.
Example 1: Given parallelograms ABCD and WXYZ below, answer the following questions.
a. Find the missing angle and side measures of each parallelogram, and label them on the diagrams.
b. Write the congruence statements for the angles of ABCD and WXYZ.
c. Find the ratios of the corresponding sides.
d. Are parallelograms ABCD and WXYZ similar? If so, write the similarity statement, and determine the
scale factor.
Geometry 300
Name__________________
7-3 Similar Polygons
Date___________________
Example 2: List the all pairs of congruent angles and write the statement of proportionality for STU ~ CDE .
Example 3: Quadrilateral PQRS is similar to quadrilateral ABCD.
P
B
Q
7
S
C
A
x
8
D
12
R
a. Find the value of x.
b. Find the scale factor of ABCD : PQRS.
Example 4: Contractors refer to blueprints when constructing a house. The blueprint below is similar to the floor
plan of a constructed house. One inch on the blueprint represents 16 feet in the actual house. Using the
properties of similar figures, determine the dimensions of the house.
.75 in
1 in
1.25 in
.5 in
Dining
Room
Kitchen
Utility
Room
.75 in
1 in
1.25 in
.5 in
Dining
Room
Kitchen
Utility
Room
Stairs
Living Room
1.25 in
Stairs
Living Room
1.25 in
Garage
Garage
1.5 in
Legend
1.5 in
Legend
: windows
: front door
: windows
: front door
Geometry 300
7-3 Similar Polygons
Name__________________
Date___________________
Practice
1. Are the triangles below similar? If so, state the proportions of similarity, and the scale factor.
2. If
,
, and
, what is
?
3. The Rivera family bought a new tent for camping. Their old tent had equal sides of 10 feet and a floor width of 15 feet,
as shown in the accompanying diagram.
If the new tent is similar in shape to the old tent and has equal sides of 16 feet, how wide is the
floor of the new tent?
4. In the accompanying diagram,
What is the length of
?
is similar to
,
,
,
, and
5. The accompanying diagram shows two similar triangles.
Which proportion could be used to solve for x?
1)
2)
3)
4)
.
Geometry 300
7-3 Similar Polygons
Name__________________
Date___________________
Homework
1. Describe the difference between congruence and similarity.
2. Must two congruent figures be similar? Explain.
3. Can two similar figures be congruent? Explain.
4. Triangle DEF has a perimeter of 25 meters and is similar to triangle PQR with a perimeter of 35 meters.
a. What is the scale factor of triangle DEF to triangle PQR?
b. What is the ratio of the angles?
c. What is the ratio of the perimeters?
d. If DE = 6 meters, find PQ.
e. Using the same scale factor, if the perimeter of PQR is 168 meters, what is the perimeter of DEF?
5. List the all pairs of congruent angles and write the statement of proportionality for
quadrilateral QRST ~ quadrilateral ABCD.
Determine whether each pair of figures is similar. Justify your answer.
6.
7.
Geometry 300
7-3 Similar Polygons
Name__________________
Date___________________
Given quadrilateral LEFT ~ quadrilateral CORK, find each of the following:
8. Scale factor of LEFT to CORK
9. KR
10. RO
11. CO
12. Perimeter of LEFT
13. Perimeter of CORK
14. Ratio of the perimeters of LEFT and CORK
15. Given DEC ~ DAB with EC AB , mA  25 , mDCE  80 , AE = 6, AD = 10, and DC = 5,
find each of the following:
D
a. m1 
b. m2 
c. m3 =
d. DB =
2
E
A
16. Two similar polygons are shown. Find the values of x and y.
1
C
3
B