Similar Polygons - Nexuslearning.net
Similar Polygons - Nexuslearning.net
Similar Polygons - Nexuslearning.net
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xy xy<br />
Using<br />
Algebra<br />
GUIDED PRACTICE<br />
Vocabulary Check ✓<br />
Concept Check ✓<br />
Skill Check ✓<br />
THEOREM<br />
THEOREM 8.1<br />
If two polygons are similar, then the ratio<br />
of their perimeters is equal to the ratios of<br />
their corresponding side lengths.<br />
If KLMN ~ PQRS, then<br />
KL<br />
= = <br />
PQ<br />
LM<br />
= <br />
QR<br />
MN<br />
= <br />
RS<br />
N<br />
N<br />
KL + LM + MN + NK<br />
<br />
K<br />
PQ + QR + RS + SP<br />
.<br />
SP<br />
EXAMPLE 5<br />
Using <strong>Similar</strong> <strong>Polygons</strong><br />
Quadrilateral JKLM is similar to<br />
quadrilateral PQRS.<br />
Find the value of z.<br />
SOLUTION<br />
Set up a proportion that contains PQ.<br />
KL JK<br />
= QR<br />
PQ<br />
Write proportion.<br />
15<br />
= <br />
6<br />
10<br />
<br />
z<br />
Substitute.<br />
z = 4 Cross multiply and divide by 15.<br />
1. If two polygons are similar, must they also be congruent? Explain.<br />
Decide whether the figures are similar. Explain your reasoning.<br />
2. 3.<br />
15<br />
In the diagram, TUVW ~ ABCD.<br />
4. List all pairs of congruent angles and write the<br />
statement of proportionality for the polygons.<br />
5. Find the scale factor of<br />
TUVW to ABCD.<br />
6. Find the length of TW Æ .<br />
7. Find the measure of TUV.<br />
8<br />
3<br />
10<br />
W<br />
K<br />
J 10<br />
M<br />
L<br />
K<br />
6<br />
89<br />
5<br />
82<br />
7<br />
87<br />
4<br />
M<br />
T 15 U<br />
23<br />
15<br />
10<br />
D<br />
6<br />
V<br />
S<br />
L<br />
89<br />
82<br />
A<br />
P<br />
12<br />
14<br />
102<br />
8.3 <strong>Similar</strong> <strong>Polygons</strong> 475<br />
q<br />
q<br />
6<br />
z<br />
R<br />
P<br />
R S<br />
9 B<br />
70<br />
C<br />
8
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