Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but possibly different sizes. This means their corresponding angles are equal and their corresponding sides are in proportion.

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What does the AA Similarity Postulate state?

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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 does the SAS Similarity Theorem state?

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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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What does the SSS Similarity Theorem state?

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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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How can you determine if two triangles are similar?

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

Front

If triangle ABC is similar to triangle DEF, what can be said about their angles?

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If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.

Front

If triangle ABC is similar to triangle DEF and AB = 6, AC = 8, and DE = 12, what is the length of DF?

Back

Since the triangles are similar, the sides are proportional. Therefore, DF = (DE/AB) * AC = (12/6) * 8 = 16.

Front

What is the relationship between the areas of two similar triangles?

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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.

Front

If triangle JKL is similar to triangle MNO and the ratio of JK to MN is 2:3, what is the ratio of their areas?

Back

The ratio of their areas is (2/3)² = 4/9.

Front

What is the significance of the included angle in the SAS Similarity Theorem?

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The included angle must be equal for the SAS Similarity Theorem to apply, ensuring that the triangles maintain their shape.