Congruent and Similar Triangles
Modelling with Similar Triangles
RECALL:
Similar triangles have exactly the same _____________ but different ____________.
IF [pic]
THEN 1. Corresponding Angles are equal. 2. Sides are Proportional.
_______________________ ________________________
_______________________
_______________________ ________________________
If n represents the scale factor then the length of any side ( or altitude) is equal to n times the length of the corresponding side ( or altitude) in the other triangle.
Similarly the perimeter of [pic] is equal to n times the perimeter of [pic].
| |CONGRUENCY |SIMILARITY |
|SYMBOL | | |
|MINIMUM | | |
|CONDITIONS | | |
| | | |
| | | |
| | | |
Examples:
A 3.6m ladder is leaning against a wall with its base 2m from the wall.
a) Determine how high up the wall the ladder reaches.
b) Suppose a 2.4m ladder is placed against the wall parallel to the longer ladder. How far will it reach up the wall and how far will its base be from the wall?
Given [pic], solve for the unknowns indicated.
3. Calculate the width of this river.
4. Jack made a scale drawing of his bedroom using a scale factor 1 cm = 0.5 m. If his drawing is 22cm by 28 cm ( regular paper)
state the scale factor as a ratio.
calculate the perimeter and area of Jack’s room.
-----------------------
C
89[pic]
[pic]
32[pic]
z
w
y
7 cm
9 cm
x
5 cm
4 cm
S
M
J
K
G
5.5m
20 m
8 m
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