Triangle Congruence

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What does congruence mean in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. If two triangles are congruent, all corresponding sides and angles are equal.

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What is the SSS (Side-Side-Side) Congruence Theorem?

Back

The SSS Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

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What is the SAS (Side-Angle-Side) Congruence Theorem?

Back

The SAS Congruence Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

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What is the ASA (Angle-Side-Angle) Congruence Theorem?

Back

The ASA Congruence Theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

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What is the HL (Hypotenuse-Leg) Congruence Theorem?

Back

The HL Congruence Theorem applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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What is the AAA (Angle-Angle-Angle) condition?

Back

The AAA condition states that if two triangles have equal corresponding angles, they are similar but not necessarily congruent.

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Back

Front

What is the relationship between the angles of congruent triangles?

Back

The corresponding angles of congruent triangles are equal. If two triangles are congruent, then all their corresponding angles are equal.

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

Back

To prove two triangles are congruent using the SSS theorem, measure all three sides of both triangles and show that they are equal.

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What is the significance of the included angle in the SAS theorem?

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In the SAS theorem, the included angle is the angle formed between the two sides being compared. It is crucial for establishing congruence.