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Determining whether two triangles are similar? - Answers
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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Determining whether two triangles are similar? - Answers
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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Determining whether two triangles are similar? - Answers
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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