Download Geometry Notes 7-2 Ratios in Similar Polygons Recall, in congruent

Geometry Notes
7-2 Ratios in Similar Polygons
Recall, in congruent polygons, corresponding sides were congruent and corresponding angles
were congruent.
We also have a relationship called similar polygons.
The following pairs of polygons are similar.
In similar polygons, corresponding angles are congruent and corresponding sides are
proportional. (In other words, the figures are the same shape but not the same size.)
Ex. 1: Determine if the triangles are similar.
If so, list the pairs of congruent angles and the
corresponding sides. Then write the similarity
statement.
Are all the pairs of angles congruent?
m∠M = m∠T = 90 − 63 = 27°, so yes.
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Are the sides proportional?
1 2 2.2
= =
(All = 2) so yes.
.5 1 1.1
Congruent Angles
∠M and ∠T
∠N and ∠Q
∠P and ∠R
Corresponding Sides
MN and TQ
NP and QR
MP and TR
The triangles are similar, and we write this as ΔMNP ~ ΔTQR .
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Ex. 2: Determine if the two figures are similar. If so, write the similarity ratio and the similarity
statement.
a) Rectangles have 4 right angles, so their angles are
congruent.
6 9
3
=
yes - similarity ratio =
4 6
2
Both are rectangles.
Similarity statement: ABCD ~ EFGH
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b) Triangle PQR is isosceles, so its base angles are equal.
180 − 36 144
m∠P = m∠R =
=
= 72°
2
2
Those are NOT the same as the base angles in triangle
STW, so the figures are not similar.
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Ex. 3: ABCD~EFGH. Solve for x.
4 6
=
x 8
6x = 4 (8) = 32
32
x=
= 5.3
6
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A
D
4
B
H
E
x
6
C
F
8
G
C
x+6
D
3
Ex. 4: ABC~EDF. Solve for x.
E
A
x+2
5
B
x+2 3
=
x+6 5
5( x + 2) = 3( x + 6)
F
5x + 10 = 3x + 18
2x = 8
x=4
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1
. If the
30
length of the model is 10 inches, what is the length of the actual sailboat in feet?
Ex. 5: The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is
1 10 in
=
30 x in
x = 30(10 in) = 300 in
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BUT the question asked for the answer in feet, so we need to convert inches to feet.
300 in ÷12 in/ft = 25 ft
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