Similar Triangles

Two triangles are similar if they have the same shape but different size.

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Their corresponding angles are equal.

Two triangles are similar if:

Similar Angles

Their corresponding sides are proportional, that is to say, they have the same ratio.

Triangle Ratios

The perimeters of similar triangles have the same ratio.

Triangle Ratios

The ratio of areas of similar triangles is equal to the square of the ratio.

Triangle Ratios

Problems

1. Calculate the height of a building that casts a shadow of 6.5 meters if at the same time and in the same place a pole of 4.5 m in height produces a shadow of 0.90 m.

Triangle Word Problems

Triangle Operations


2.The legs of a right triangle measure 24 m and 10 m. What is the length of the legs of a similar triangle to this one whose hypotenuse is 52 m?

Similar Triangles

Triangle Operations

Triangle Operations

Triangle Operations


Similar Triangle Rules

1Two triangles are similar if two angles are equal.


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Angle Ratios

 

2 Two triangles are similar if the sides are proportional.


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Triangle Ratios

 

3 Two triangles are similar if two sides are proportional and the angle between them is equal.


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Examples

Determine whether the following triangles are similar:

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Triangle Operations

Triangle Operations

Triangle Operations

The triangles are similar because the sides are proportional.


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180º − 100º − 60º = 20º

They are similar triangles because they have two equal angles.


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formulas

They are similar because two sides are proportional and the angle between them is equal.


Similar Right Triangles

1Two right triangles are similar if they have an equal acute angle.

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Angle Ratios


2Two right triangles are similar if they have two legs that are proportional.

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Triangle Ratios


3Two right triangles are similar if the ratio of the hypotenuses and the legs are proportional.

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Triangle Ratios