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If two triangles have the same shape but one is an enlargement of the other they are said to be similar. The two triangles must be equi-angular.

To prove that ∆ABC is similar to ∆XYZ it is necessary to prove one of the following :-

1) Two angles in ∆ABC are equal to two angles in ∆XYZ, since it follows that the third angles will also be equal.

2) The three sides of ∆ABC are proportional to the corresponding sides of ∆XYZ

AB/XY = AC/XZ = BC/YZ

3) Two sides in ∆ABC are proportional to two sides in ∆XYZ and the angles included between these sides in each triangle are equal.

AB/XY = AC/XZ and angle A = angle X.

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15y ago

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