Triangle Congruency - Modified

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What does ASA stand for in triangle congruency?

Back

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

Front

What does AAS stand for in triangle congruency?

Back

AAS stands for Angle-Angle-Side, a theorem 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, then the triangles are congruent.

Front

What does SAS stand for in triangle congruency?

Back

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

Front

What does SSS stand for in triangle congruency?

Back

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

Front

What does HL stand for in triangle congruency?

Back

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

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Back

The corresponding sides and angles of triangles ABC and DEF are equal.

Front

How can you determine if two triangles are congruent using the ASA postulate?

Back

To determine if two triangles are congruent using the ASA postulate, check if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

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What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

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What is the relationship between congruency and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent. Congruent triangles have equal corresponding sides and angles, while similar triangles have proportional sides and equal corresponding angles.

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Provide an example of a situation where you would use the AAS theorem to prove triangle congruency.

Back

If you know two angles of triangle XYZ are 50° and 60°, and the side opposite the 50° angle is 5 cm, you can use the AAS theorem to prove triangle XYZ is congruent to another triangle with the same angle measures and corresponding side.