What is a polygon? What are the different types of polygons? What is a congruent polygon? What is...
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Transcript of What is a polygon? What are the different types of polygons? What is a congruent polygon? What is...
What is a polygon?
What are the different types of polygons?
What is a congruent polygon?
What is a similar polygon?
What are some examples of these polygons?
A polygon is a plane having three or more sides.
Convex polygon: all the sides are pushed outward.Concave polygon: at least two sides are pushed inward.Regular polygon: all the sides have the same length and their angles are all the same size.
Take a minute to match the name up with the figure . . .
Congruent polygons are polygons that have the same size and the
same shape.
fact:
fact: Congruent shapes have all their sides and angles congruent.
Notice how the second figures have the same shape
and size of the first – they match exactly.
Now we are going to take a look at similar polygons . . .
Can you find similar polygons?
(1) Triangle
(2) Rectangle
(3) Pentagon
(4) Hexagon
(5) Octagon
Same shape
Different size
Angle does not change
Enlargement
Reduction
Definition: Figures that have exactly same shape are called similar figures.
(1) In polygons, the size of angles does not change.
(2) One figure is an enlargement or reduction of the other.
(3) Congruent figures are similar because they gave the same shape.
Properties:
How can we know the length of sides in similar figures?
If two figures are similar, one figure is an enlargement of the other. The size-change factor tells the amount of enlargement or reduction.
Example 1: If a copy machine is used to copy a drawing or picture, the copy will be similar to the original.
Original Copy
Exact Copy
Copy machine set to 100%
Size-change factor is
Original Copy
Enlargement
Copy machine is set to 200%
Size-change factor is
Original Copy
Reduction
Copy machine is set to 50%
Size-change factor is1X 2X
1
2x
Example 2: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO?
C
A
T G
O
D
1.5 cm
3 cm
2 cm
3 cm
6 cm
? cm
Each side and its enlargement form a pair of sides called corresponding sides.
(1) Corresponding side of TC --> GD
(2) Corresponding side of CA--> DO
(3) Corresponding side of TA--> GO
Length of
corresponding sides
GD=3
TC=1.5
DO=6
CA=3
GO=?
TA=2
Ratio of Lengths 3/1.5=2 6/3=2 ?/2=2
The size-change factor is 2x.
(1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle.
1.5 cm
2 cm
3 cm
T
C
A
G
D
O3 cm
6 cm
? cm
(2) Now, let’s find the length of side GO
i) What side is corresponding side of GO? TA
ii) What is the size-change factor? 2X
iii) Therefore, GO= size-change factor x TA
iv) So, GO= 2 x 2 = 4 cm
Same shapeDifferent size
Corresponding side Size-change factor
Not change angle
Similar polygons
Example 1: Quadrangles ABCD and EFGH are similar. How long is side AD? How long is side GH?
15 cm
? cm
18 cm
12cm7cm
6cm
4cm
?cm
BC
A
D
H
E
GF
(1) What is size-change factor?
(2) What is corresponding side of AD ?
(3) How long is side AD?
(4) What is corresponding side of GH?
(5) How long is side GH?
12÷ 4= 3 & 18÷ 6=3
EH
AD = 5
CD
7 x 3 = GH, GH = 21
A polygon is a plane having three or more sides.
Congruent polygons are polygons that have the same size and the same shape.
Similar polygons are polygons that have the same shape.
congruent congruent
similar similar
Circle Limit IIICircle Limit IIIM.C. EscherM.C. Escher
Similar figures look alike but one is a smallerSimilar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me.version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing It wouldn’t make much sense to make a drawing of this ship the actual size of the ship. of this ship the actual size of the ship.
Just like congruent polygons, the correspondingangles in similar polygons must be congruent.
AA XX
CCDD
BB WW
ZZ YY
A = 80° B = 30° Z = 170°A = 80° B = 30° Z = 170°
W = ___ X = ___ D = ___W = ___ X = ___ D = ___80°80° 30° 170°170°
The sides are a little different.The sides are a little different.
They must be They must be PROPORTIONAL.PROPORTIONAL.
AA XX
CCDD
BB WW
ZZ YY
ABAB = = BCBC = = CDCD = = DADA
WX XYWX XY YZ ZWYZ ZW
This means I should be able to multiply each sideThis means I should be able to multiply each sideof the smaller polygon by the same number andof the smaller polygon by the same number andget it’s corresponding side on the bigger polygon.get it’s corresponding side on the bigger polygon.
444x2 = 84x2 = 8
555x2 = 105x2 = 10
222x2 = 42x2 = 4
333x2 = 63x2 = 6
The The SCALE FACTORSCALE FACTOR is the ratio is the ratio of the corresponding sidesof the corresponding sides
SMALLSMALL BIGBIG BIG SMALLBIG SMALL
oror
What is the scale factor of these polygons?What is the scale factor of these polygons?
1010
44
XX 77
YY88
ZZ66
Scale FactorScale Factor = = 101044
== 5522
44
77
YY
ZZ
1010
XX
88
66
101044
== 5522
Use the scale factor to find the other sidesUse the scale factor to find the other sides
55 662 Z2 Z==
5z = 125z = 12 z = z = 1212 = 2.4 = 2.4 55
SF =SF =
55 XX2 72 7
2x = 352x = 35 x = x = 35 35 = 17.5= 17.5 22
== 55 882 Y2 Y
5y = 165y = 16 y = y = 1616 = 3.2 = 3.2 55
==