similar and congruent. congruent figures in order to be congruent, two figures must be the same size...
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SIMILA
R AND C
ONGRUENT
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CONGRUENT FIGURES
In order to be congruent, two figures must be the same size and same shape.
~ =
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WHAT ARE SIMILAR POLYGONS?
Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.
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SIMILAR FIGURES
Similar figures must be the same shape, but their sizes may be different. They have to be what we call proportional.
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ANGLES AND SIDES IN SIMILAR POLYGONS
Angles
∠A ≅ ∠ E
∠B ≅ ∠ F
∠C ≅ ∠ G
ΔABC ~ ΔEFGA
B C
E
F G
Sides
AB ~ EF
AC ~ EG
BC ~ FG
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PROPORTIONAL?
• In order for a figure to be considered proportional the figures have their sides have to create the same reduced fraction.
12 in.
20 in.
4 in.
5 in.
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SIMILAR? CONGRUENT? NEITHER?
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SIMILAR? CONGRUENT? NEITHER?
5 5
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SIMILAR? CONGRUENT? NEITHER?
7 42
5 40
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SIMILAR? CONGRUENT? NEITHER?
72
9
14
112
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PROPORTIONS
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YOU CAN FIND THE MISSING LENGTH OF A SIDE IN A PAIR OF SIMILAR FIGURES, BY USING PROPORTIONS
6 7
ΔRST ~ ΔUVW
R
ST
U
V W
x ft.
6 ft.
35 ft. 7 ft.
35=x x = 30 feet
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SOLVE FOR X.
x 30
12 in.x in.
40 in. 30 in..
40=12 x = 9 inches
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SOLVE FOR X. ROUND TO THE NEAREST TENTH.
4 x
12 in.
4 in.
20 in.
x in..
20=12 x = 6.7 inches
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SOLVE FOR X.
7 25
14 m.7 m.
x 25 m.
x=14 x = 50 meters
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SOLVE FOR X. ROUND TO THE NEAREST TENTH.
15 x
17 in.
x
35 in.
15 in.
17=35 x = 7.3 inches
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DETERMINE THE MISSING SIDES OF THE TRIANGLE
Click to edit Master text styles Second level
Third level Fourth level
Fifth level
39 in
24 in
33 in
? in
8 in
? in
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SIMILA
R FIG
URES
PRACTI
CE
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12
3
28X
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15
6
24
y
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14
2
1b
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48 6
9t
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126 14
12G
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84
12
8
D