Triangle Congruence

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What is Triangle Congruence?

Back

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

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What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a rule that states 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.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a rule that states 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.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a rule that states 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.

Front

What does SSS stand for in triangle congruence?

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

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What is the significance of the SSA condition in triangle congruence?

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SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

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What is the HL theorem in triangle congruence?

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HL stands for Hypotenuse-Leg, a rule that applies 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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Can triangles be congruent if they have the same angles but different side lengths?

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No, triangles cannot be congruent if they have the same angles but different side lengths; this is known as the AAA condition, which does not imply congruence.

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What is the difference between congruent triangles and similar triangles?

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Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size, with corresponding angles equal and sides in proportion.

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How can you prove two triangles are congruent using the SSS rule?

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To prove two triangles are congruent using the SSS rule, you must show that all three sides of one triangle are equal to the corresponding three sides of the other triangle.