Triangle Congruence & Similarity

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What is Triangle Congruence?

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Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning all corresponding sides and angles are equal.

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What is Triangle Similarity?

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Triangle similarity occurs when two triangles have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their sides are in proportion.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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What does SAS stand for in triangle congruence?

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SAS stands for Side-Angle-Side, a theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

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What does ASA stand for in triangle congruence?

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ASA stands for Angle-Side-Angle, a theorem stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

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What does AAS stand for in triangle congruence?

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AAS stands for Angle-Angle-Side, a theorem stating that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.

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What does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem applicable to right triangles stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

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What is the AA criterion for triangle similarity?

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The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

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How do you determine if triangles are similar using proportions?

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To determine if triangles are similar using proportions, compare the ratios of the lengths of corresponding sides. If the ratios are equal, the triangles are similar.

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What is the relationship between similar triangles and their areas?

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The areas of similar triangles are proportional to the square of the lengths of their corresponding sides.