Geometry Test For Similar Triangles
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Test For Similar Triangles

 

 Sometimes we have two triangles that are the same shape,

 but one is bigger than the other.
 When we have this,
 the angles will be the same in each triangle.
 The length of the sides, however, will not be the same.
 

 
 The triangle on the right has the same angles 
 as the triangle on the left, but is twice as big.
 These triangles are similar.
 

 
 In the triangle on the right, the sides are 1.5 times as long
 as the sides in the triangle on the left.
 These triangles are similar.
 
 So in similar triangles, the angles are the same.
 Each of the sides in the bigger triangle
 are equal to the length of the sides in the smaller triangle
 times some number.
 That number is the ratio of the length of the sides.
 An easy way to find the ratio of the side length
 between two similar triangles is to take the length
 of one of the sides in the bigger triangle
 and divide it by the length of the CORRESPONDING side
 in the smaller triangle.
 

 
 If two triangles with the same angles are the same size,
 we can call them similar if we want.
 But we say more if we call them congruent,
 so that's what we usually do.
 
 (Maybe you can guess what's coming next ...)
 
 Usually we don't know the length of all of the sides.
 We usually don't know the measure of all of the angles
 So just what do we need to know?
 
 Well. any of the theorems that showed that two triangles are congruent
 also show that they are similar, but there are others ...
 
 
 ANGLE - ANGLE - ANGLE
 If all three angles of one triangle 
 are the same as all three angles of the other triangle,
 the triangles are similar.
 
 ANGLE - ANGLE
 If we know that two angles of one triangle 
 are the same as two of the angles of the other triangle,
 the triangles are similar.
 (This one is kind of cheezy. If we know 2 angles we actually know all 3)
 
 SIDE - ANGLE - SIDE
 

 
 When we know two sides 
 and the angle between them in two triangles and ...
 1) The angles are the same
 2) The ratio of the corresponding sides are the same
 Then the triangles are congruent.
 

   copyright 2005 Bruce Kirkpatrick

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