Triangle Proportionality Theorem

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What is the Triangle Proportionality Theorem?

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The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

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CCSS.HSG.SRT.A.2

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If two triangles are similar, what can be said about their corresponding sides?

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The corresponding sides of similar triangles are in proportion.

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CCSS.HSG.SRT.A.2

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What is the similarity shortcut AA?

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AA (Angle-Angle) similarity states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

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CCSS.HSG.SRT.B.5

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What does it mean for two triangles to be congruent?

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Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

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CCSS.8.G.A.2

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What is the SAS similarity criterion?

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SAS (Side-Angle-Side) similarity states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

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CCSS.HSG.SRT.B.5

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What is the SSS similarity criterion?

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SSS (Side-Side-Side) similarity states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

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CCSS.HSG.SRT.B.5

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How can you determine if two triangles are similar using the Triangle Proportionality Theorem?

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You can determine similarity by showing that the ratios of the lengths of corresponding sides are equal.

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CCSS.HSG.SRT.B.5

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What is the formula for the Triangle Proportionality Theorem?

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CCSS.HSG.SRT.B.4

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Back

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CCSS.HSG.SRT.B.4

Front

What is the relationship between similar triangles and their areas?

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The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.