Triangle Similarity w/Proofs

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the concept that two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

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What is the AA Similarity Postulate?

Back

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

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What is the SSS Similarity Theorem?

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

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What is the SAS Similarity Theorem?

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The SAS (Side-Angle-Side) Similarity Theorem states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

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How do you determine if two triangles are similar?

Back

To determine if two triangles are similar, check if they satisfy one of the similarity criteria: AA, SSS, or SAS.

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If two triangles have angles measuring 30°, 60°, and 90°, what can be said about their similarity?

Back

If two triangles have angles measuring 30°, 60°, and 90°, they are similar by the AA Similarity Postulate.

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What is a scale factor in triangle similarity?

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A scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

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If triangle ABC is similar to triangle DEF, and AB = 6 cm, DE = 9 cm, what is the scale factor?

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The scale factor is 9/6 or 3/2.

Front

How can you use proportions to find missing side lengths in similar triangles?

Back

You can set up a proportion using the lengths of corresponding sides to find the missing side length.

Front

If two triangles are similar and one triangle has a side length of 4 cm, and the corresponding side in the other triangle is 8 cm, what is the ratio of their areas?

Back

The ratio of their areas is (8/4)² = 4:1.