Triangle Similarity

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What is Triangle Similarity?

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Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are in proportion.

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What does AA Similarity stand for?

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AA Similarity stands for Angle-Angle Similarity. It 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 SSS Similarity stand for?

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SSS Similarity stands for Side-Side-Side Similarity. It states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

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What does SAS Similarity stand for?

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SAS Similarity stands for Side-Angle-Side Similarity. It states that if two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, then the triangles are similar.

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How can you determine if two triangles are similar using AA?

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To determine if two triangles are similar using AA, check if two angles of one triangle are equal to two angles of another triangle. If they are, the triangles are similar.

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

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If triangle ABC is similar to triangle XYZ, then angle A = angle X, angle B = angle Y, and angle C = angle Z.

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If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

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Yes, triangle ABC and triangle DEF are similar by SSS Similarity because the sides are in proportion (3:6, 4:8, 5:10).

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What is the relationship between corresponding sides of similar triangles?

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The corresponding sides of similar triangles are in proportion, meaning the ratio of the lengths of corresponding sides is constant.

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If triangle ABC is similar to triangle DEF and the length of side AB is 5 cm and side DE is 10 cm, what is the ratio of similarity?

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The ratio of similarity is 1:2, since 5 cm to 10 cm simplifies to 1:2.

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What is the height of a tree if it casts a shadow of 10 m and a similar triangle casts a shadow of 5 m with a height of 2 m?

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The height of the tree is 4 m, using the proportion of similar triangles (height of tree / 10 m = 2 m / 5 m).