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MPM2D
U06L01
Congruent and Similar Triangles
When comparing 2 triangles, they are either: congruent, similar or neither
1) Congruent Triangles: have the exact same Size and Shape ( )
ALL CORRESPONDING SIDES AND ANGLES ARE EQUAL
2) Similar Triangles: have the same SHAPE but are DIFFERENT sizes (one triangle is an enlargement or reduction of the other). The symbol used to indicate similarity is ~
PROPERTIES OF SIMILAR TRIANGLES
D
A
6 cm
2 cm
B
4 cm
12 cm
4 cm
C
E
8 cm
F
Δ
If ABC and DEF are similar...
Δ
i)
the corresponding pairs of angles are equal
ii) the ratios of the corresponding sides are equal
iii) the ratios of the areas is equal to the ratio of their squares of their corresponding sides
MPM2D
U06L01
CONDITIONS FOR SIMILARITY
A
D
B
F
C
E
i)
SSS: 3 pairs of corresponding sides are proportional
ii) SAS: 2 pairs of corresponding sides are proportional and the contained angles are equal
iii) AA~: 2 pairs of corresponding angles are equal
Example # 1: a) Show that ABC EDC.
Δ
Δ
To demonstrate similarity;
SSS~ not enough information
SAS~ not in this situation
AA~ use this one
b) Find the lengths of x and y.
A 7 cm B
statement
4 cm
5 cm
authority
opposite angle theorem
C
6 cm
D
x
y
parallel line theorem
­alternate angles (Z pattern)
E
Because they are similar, the corresponding
sides must be proportional.
parallel line theorem
­alternate angles (Z pattern)
Homework: p. 460 # 1 - 4 , 5ac , 6ac , 7ac , 10