Properties of Similar Triangles

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What is the definition of similar triangles?
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Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
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What is the symbol used to denote similarity between triangles?
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The symbol '~' is used to denote similarity between triangles.
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If two triangles are similar, what can be said about their angles?
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All corresponding angles of similar triangles are equal.
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How do the sides of similar triangles compare to each other?
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The lengths of corresponding sides of similar triangles are in proportion.
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What is the AA criterion for triangle similarity?
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Two triangles are similar if two pairs of corresponding angles are equal.
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What is the SSS criterion for triangle similarity?
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Two triangles are similar if all three pairs of corresponding sides are in proportion.
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What is the SAS criterion for triangle similarity?
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Two triangles are similar if two pairs of sides are in proportion and the included angle is equal.
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How do you find the scale factor between two similar triangles?
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The scale factor is the ratio of any pair of corresponding sides of the similar triangles.
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Can right triangles be similar to other right triangles?
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Yes, right triangles can be similar if they meet the angle-similarity or side-similarity criteria.
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How does similarity of triangles relate to real-world applications?
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Similar triangles can be used in real-world applications such as determining heights of tall objects using indirect measurements.
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If triangle ABC ~ triangle DEF and AB = 4, AC = 6, DE = 8, what is DF?
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DF = 12, using the proportion (AB/DE = AC/DF).
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What is a practical method to test triangle similarity in construction?
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Builders often use a ruler and a protractor to check angle measures and side lengths for similarity.
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If the ratio of the perimeters of two similar triangles is 1:3, what is the ratio of their areas?
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The ratio of their areas is 1:9 because the area ratio is the square of the perimeter ratio.
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Can two equilateral triangles be considered similar? Why?
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Yes, all equilateral triangles are similar to each other because they have equal angles and proportional sides.
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What role does the centroid play in similar triangles?
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In similar triangles, the centroid divides each median in a ratio of 2:1, regardless of the size of the triangles.
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