2 triangles are stated to be similar if their matching angles space congruent and also the corresponding sides room in relationship . In various other words, similar triangles are the exact same shape, yet not necessarily the exact same size.

The triangles room congruent if, in addition to this, their corresponding sides space of equal length.

The side lengths of two comparable triangles room proportional. The is, if Δ U V W is comparable to Δ X Y Z , then the following equation holds:

U V X Y = U W X Z = V W Y Z

This typical ratio is called the scale factor .

The symbol ∼ is provided to show similarity.

Example:

Δ U V W ∼ Δ X Y Z . If U V = 3 , V W = 4 , U W = 5     and also     X Y = 12 , discover X Z and also Y Z .

attract a figure to assist yourself visualize.

create out the proportion. Make sure you have actually the matching sides right.

3 12 = 5 X Z = 4 Y Z

The scale element here is 3 12 = 1 4 .

fixing these equations gives X Z = 20 and Y Z = 16 .

The ideas of similarity and scale aspect can be prolonged to other figures besides triangles.

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