6.4 Similar Polygons
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6.4 Similar Polygons 6.4 Similar Polygons Geometry Mr. Jimenez Spring 2011
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6.4 Similar Polygons. Geometry Mr. Jimenez Spring 2011. When there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons are called similar polygons. - PowerPoint PPT Presentation
Transcript of 6.4 Similar Polygons
6.4 Similar Polygons6.4 Similar PolygonsGeometry
Mr. JimenezSpring 2011
Identifying similar polygonsIdentifying similar polygonsWhen there is a correspondence between
two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons are called similar polygons.
In the next slide, ABCD is similar to EFGH. The symbol ~ is used to indicate similarity. So, ABCD ~ EFGH.
Ex. 1: Writing Similarity Ex. 1: Writing Similarity StatementsStatementsPentagons JKLMN and STUVW are similar.
List all the pairs of congruent angles. Write the ratios of the corresponding sides in a statement of proportionality.
J K
L
M
N
LU
M
VN
W
S T
U
V
W
J K S T
Ex. 1: Writing Similarity Ex. 1: Writing Similarity StatementsStatements
J K
L
M
N
S T
U
V
W
Because JKLMN ~ STUVW, you can write J S, K T, L U, M V AND N W.
You can write the proportionality statement as follows:
KL
TU=
JK=
ST
MN
VW=
LM=
UV
NJ
WS
J SK T
L
U
M
VN
W
Ex. 2: Comparing Similar Ex. 2: Comparing Similar PolygonsPolygons
Decide whether the figures are similar. If they are similar, write a similarity statement.
15
12
9
6X
W
Z
Y
10
8
6
4Q
P
S
R
15
12
9
6X
W
Z
Y
10
8
6
4Q
P
S
RSOLUTION:
As shown, the corresponding angles of WXYZ and PQRS are congruent. Also, the corresponding side lengths are proportional.
WX
PQ=
15
10=
3
2
XY
QR=
6
4=
3
2
YZ
RS=
9
6=
3
2
WX
PQ=
15
10=
3
2So, the two figures are similar and you can write WXYZ ~ PQRS.
Ex. 3: Comparing Photographic Ex. 3: Comparing Photographic EnlargementsEnlargements
POSTER DESIGN. You have been asked to create a poster to advertise a field trip to see the Liberty Bell. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be?
Solution:Solution:
To find the length of the enlargement, you can compare the enlargement to the original measurements of the photo.
16 in.
3.5 in.=
x in.
5 in.
x = 16
3.5x∙ 5
x ≈ 22.9 inches
The length of the enlargement will be about 23 inches.
5
3.5
Using similar polygons in real lifeUsing similar polygons in real lifeIf two polygons are similar, then the
ratio of lengths of two corresponding sides is called the scale factor. In Example 2 on the previous page, the common ratio of is the scale factor of WXYZ to PQRS.
3
2
Ex. 4: Using similar polygonsEx. 4: Using similar polygonsThe rectangular
patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters.
16 ft 24 ft32 ft
48 ft
Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft. , which is 3:2 in simplified form.
The perimeter of the patio is 2(24) + 2(48) = 144 feet and the perimeter of the pool is 2(16) + 2(32) = 96 feet The ratio of the perimeters is =
16 ft 24 ft32 ft
48 ft
14496
3
2
, or
NOTE:NOTE:
Notice in Example 4 that the ratio of perimeters is the same as the scale factor of the rectangles. This observation is generalized in the following theorem.
Ex. 5: Using Similar PolygonsEx. 5: Using Similar PolygonsQuadrilateral JKLM is
similar to PQRS. Find the value of z.
Set up a proportion that contains PQ
15
10J
M L
KZ
6
S
PQ
R
KLQR
JKPQ
=
156
10Z
=
Z = 4
Write the proportion.
Substitute
Cross multiply and divide by 15.
Homework:Study page 377,
384 for test tomorrow!
