Just Congruent Triangles

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SSS postulate state?

Back

The SSS (Side-Side-Side) postulate states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does the SAS postulate state?

Back

The SAS (Side-Angle-Side) postulate 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.

Front

What does the ASA postulate state?

Back

The ASA (Angle-Side-Angle) postulate 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.

Front

What is the AAS theorem?

Back

The AAS (Angle-Angle-Side) theorem states 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, then the triangles are congruent.

Front

What is the HL theorem?

Back

The HL (Hypotenuse-Leg) theorem states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.

Front

What is the significance of the SSA condition?

Back

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

Front

What is the difference between congruence and similarity in triangles?

Back

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

Front

How can you determine if two triangles are congruent using their angles?

Back

If two triangles have two pairs of equal angles, they are congruent by the AAS or ASA postulates.

Front

What is the role of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which is essential for establishing triangle congruence.