Triangle Congruence

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What does AAS stand for in triangle congruence?

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

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What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states if two sides and the included angle of one triangle are congruent to two sides and the corresponding included angle of another triangle, then 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 that states if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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The second triangle could be XYZ, ZYX, or YXZ, depending on the order of the vertices.

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The second triangle could be CBA, ABC, or CAB, depending on the order of the vertices.

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What is the significance of congruence statements in geometry?

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Congruence statements indicate that two triangles are identical in shape and size, allowing for the transfer of properties and measurements between them.

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How can you prove triangles are congruent using the SSS postulate?

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To prove triangles are congruent using SSS, show that all three sides of one triangle are equal in length to the corresponding sides of another triangle.

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How can you prove triangles are congruent using the ASA postulate?

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To prove triangles are congruent using ASA, show that two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle.