Triangle Similarity

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What is Triangle Similarity?

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Triangle similarity refers to the concept that two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

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What is the Side-Angle-Side (SAS) similarity criterion?

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The SAS similarity criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

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What is the Angle-Angle (AA) similarity criterion?

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The AA similarity criterion 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 definition of a dilation in geometry?

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A dilation is a transformation that alters the size of a figure but maintains its shape, defined by a center point and a scale factor.

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Back

The lengths of the sides of the triangle will be reduced to one-third of their original lengths.

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How do you find the height of an object using similar triangles?

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You can set up a proportion using the heights and shadow lengths of two similar objects to find the unknown height.

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What is the relationship between corresponding angles in similar triangles?

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In similar triangles, all corresponding angles are equal.

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What is the relationship between corresponding sides in similar triangles?

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In similar triangles, the lengths of corresponding sides are in proportion.

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If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their corresponding sides?

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The ratio of their corresponding sides is 1:2.

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What is the definition of proportionality in the context of similar triangles?

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Proportionality in similar triangles means that the ratios of the lengths of corresponding sides are equal.