SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size...
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Transcript of SIMILAR AND CONGRUENT. CONGRUENT FIGURES In order to be congruent, two figures must be the same size...
SIMILA
R AND C
ONGRUENT
CONGRUENT FIGURES
In order to be congruent, two figures must be the same size and same shape.
~ =
WHAT ARE SIMILAR POLYGONS?
Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.
SIMILAR FIGURES
Similar figures must be the same shape, but their sizes may be different. They have to be what we call proportional.
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
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.
SIMILAR? CONGRUENT? NEITHER?
SIMILAR? CONGRUENT? NEITHER?
5 5
SIMILAR? CONGRUENT? NEITHER?
7 42
5 40
SIMILAR? CONGRUENT? NEITHER?
72
9
14
112
PROPORTIONS
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
SOLVE FOR X.
x 30
12 in.x in.
40 in. 30 in..
40=12 x = 9 inches
SOLVE FOR X. ROUND TO THE NEAREST TENTH.
4 x
12 in.
4 in.
20 in.
x in..
20=12 x = 6.7 inches
SOLVE FOR X.
7 25
14 m.7 m.
x 25 m.
x=14 x = 50 meters
SOLVE FOR X. ROUND TO THE NEAREST TENTH.
15 x
17 in.
x
35 in.
15 in.
17=35 x = 7.3 inches
DETERMINE THE MISSING SIDES OF THE TRIANGLE
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39 in
24 in
33 in
? in
8 in
? in
SIMILA
R FIG
URES
PRACTI
CE
12
3
28X
15
6
24
y
14
2
1b
48 6
9t
126 14
12G
84
12
8
D