Mathematics Magazine for Grades 1-12  

 

7/2004

     

In the practical use of our intellect, forgetting is as important as remembering.
 - William James

Grade 10

Theory:

Similar Triangles
If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.).

 

angle A = angle D
angle B = angle E
angle C = angle F

AB/DE = BC/EF = AC/DF = perimeter of ABC/ perimeter of DEF

Two triangles are similar if:
1) 3 angles of 1 triangle are the same as 3 angles of the other
or 2) 3 pairs of corresponding sides are in the same ratio
or 3) An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio.

Example:
In the above diagram, the triangles are similar. EF = 6cm and BC = 2cm . What is the length of DE if AB is 3cm?
EF = 3BC, so DE = 3AB = 9cm.

Problems with solutions.

1.        Triangles CDE and NOP are similar. The perimeter of smaller triangle CDE is 133. The lengths of two corresponding sides on the triangles are 53 and 212. What is the perimeter of NOP?

Solution:

 

 

 

 

The perimeter of NOP:

= 532

Proposed Exercises:

Complete.

1.        (-3x4 + 36x2)    (3x)

2.        (-29x3 + 116x)    (-29)

3.        (-8x4 + 76x3 - 192x2 + 60x)    (-4x)

4.        (-120x5 + 84x4 + 92x3 + 400x2 + 224x)    (4x)