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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download