MWA10 6.2 Similar Polygons

1. Determining if Two Polygons are Similar
Slide 1
Two figures are similar if:
(1) Corresponding angles are congruent
(2) Corresponding sides are proportional
B
A
C
D
110
70
4 cm
2 cm
6 cm
7 cm E
F G
H
110
70
8 cm
14 cm
4 cm
12 cm

2. Determining if Two Polygons are Similar
Slide 2
Two figures are similar if:
(1) Corresponding angles are congruent
(2) Corresponding sides are proportional
B
A
C
D
110
70
4 cm
2 cm
6 cm
7 cm E
F G
H
110
70
8 cm
14 cm
4 cm
12 cm
A and E
A = E = 110
B and F
B = F = 90
C and G
C = G = 90
D and H
D = H = 70

3. Determining if Two Polygons are Similar
Slide 3
Two figures are similar if:
(1) Corresponding angles are congruent
(2) Corresponding sides are proportional
B
A
C
D
110
70
4 cm
2 cm
6 cm
7 cm E
F G
H
110
70
8 cm
14 cm
4 cm
12 cm
2 1
4 2
AB cm
EF cm
 
6 1
12 2
BC cm
FG cm
 
4 1
8 2
CD cm
GH cm
 
7 1
14 2
DA cm
HE cm
 
Since the corresponding angles are congruent AND the ratio of the
corresponding sides equal, the polygons are similar. ABCD ~ EFGH
A and E
A = E = 110
B and F
B = F = 90
C and G
C = G = 90
D and H
D = H = 70

4. Slide 4
Example 1:
Lorinda wants to resize a photo for her
scrapbook. She has space for a photo
that is 5cm by 8cm. Will the two photos
be similar?
Original photo – 10cm by 15cm

5. Sketch diagram
Slide 5
Example 1:
Lorinda wants to resize a photo for her
scrapbook. She has space for a photo
that is 5cm by 8cm. Will the two photos
be similar?
Original photo – 10cm by 15cm
original resized
15
10 5
8

6. Sketch diagram
Slide 6
Example 1:
Lorinda wants to resize a photo for her
scrapbook. She has space for a photo
that is 5cm by 8cm. Will the two photos
be similar?
Original photo – 10cm by 15cm
original resized
15
10 5
8
Calculate ratio of corresponding sides
10
2
5
original
new
 
15
1.875
8
original
new
 
Answer:
The two photos will not be
similar because the ratios
of the corresponding sides
are not equal.Are the ratios the same? No

7. Slide 7
Example 2:
Aidan frames a 24-inch by 36-inch picture
with a 4-inch frame. Is the framed picture
similar in shape to the unframed picture?

8. Since the unframed picture and
the framed picture are both
rectangles, we know that every angle
measures 90
 Corresponding angles are congruent
Slide 8
Example 2:
Aidan frames a 24-inch by 36-inch picture
with a 4-inch frame. Is the framed picture
similar in shape to the unframed picture?

9. Since the unframed picture and
the framed picture are both
rectangles, we know that every angle
measures 90
 Corresponding angles are congruent
Slide 9
Example 2:
Aidan frames a 24-inch by 36-inch picture
with a 4-inch frame. Is the framed picture
similar in shape to the unframed picture?
Answer:
While the corresponding angles are
congruent, the ratios of the
corresponding sides are not equal.
The unframed picture and the framed
picture are NOT similar.
Now to compare ratio of corresponding sides.
4
4
4
4
24
36
24
36
unframed unframed
32
44
24 3
36 4

32 9
44 11

3 9
4 11


10. Slide 10
Example 3:
The scale on a map is 2.5 cm : 500 m.
(a) What distance is represented by a 12.5 cm segment on the map?
(b) How long would a segment on the map be if it represented 1.5 km?

11. Slide 11
Example 3:
The scale on a map is 2.5 cm : 500 m.
(a) What distance is represented by a 12.5 cm segment on the map?
(b) How long would a segment on the map be if it represented 1.5 km?
a) Let x = distance
2.5 ( ) 12.5
500 ( )
cm map cm
m distance x

2.5 6250x cm cm m 
2.5 6250
2.5 2.5
x cm cm
c
m
cm m


2500x m
(a) A 12.5 cm segment on a map
will represent a distance of 2500 m.

12. Slide 12
Example 3:
The scale on a map is 2.5 cm : 500 m.
(a) What distance is represented by a 12.5 cm segment on the map?
(b) How long would a segment on the map be if it represented 1.5 km?
a) Let x = distance
2.5 ( ) 12.5
500 ( )
cm map cm
m distance x

2.5 6250x cm cm m 
2.5 6250
2.5 2.5
x cm cm
c
m
cm m


2500x m
(a) A 12.5 cm segment on a map
will represent a distance of 2500 m.
a) Let x = segment
2.5 ( )
500 ( ) 1500
cm map x
m distance m

3750 500cm m x m 
500 5
3750
0
5 0
0
0
m m
cm m x m

7.5x cm
(b) The 1.5 km distance
will be a 7.5 cm segment.