Triangle Similarity Postulates (1st)

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What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side. It is a postulate that states 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 AA stand for in triangle similarity?

Back

AA stands for Angle-Angle. It is a postulate that states 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 SAS stand for in triangle similarity?

Back

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

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

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To determine if two triangles are similar using SSS, compare the lengths of the corresponding sides. If the ratios of the lengths of the sides are equal, 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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How can you determine if two triangles are similar using SAS?

Back

To determine if two triangles are similar using SAS, compare the lengths of two sides of each triangle. If the sides are proportional and the included angles are equal, the triangles are similar.

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What is the significance of triangle similarity in geometry?

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Triangle similarity is significant because it allows us to make conclusions about the properties of triangles based on the properties of similar triangles, such as proportionality of sides and equality of angles.

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Can two triangles be similar if they have no equal angles?

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No, two triangles cannot be similar if they have no equal angles. Similar triangles must have at least two equal angles (AA postulate) or satisfy the SSS or SAS conditions.

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

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If triangle ABC is similar to triangle DEF, then the lengths of the corresponding sides are proportional.

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If two triangles are similar, what can be said about their areas?

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If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.