PROOFS with Congruent triangles

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, triangle ABC is congruent to triangle ABC.

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 included angle of another triangle, then the triangles are congruent.

Front

What is the CPCTC Theorem?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, which means that if two triangles are proven to be congruent, then their corresponding sides and angles are also congruent.

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid postulate for proving triangle congruence because it can lead to ambiguous cases.

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 is the importance of the included angle in the SAS postulate?

Back

The included angle is crucial in the SAS postulate because it is the angle formed between the two sides being compared, ensuring that the triangles are congruent.

Front

What are the three main triangle congruence postulates?

Back

The three main triangle congruence postulates are SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle).

Front

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

Back

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

Front

What is the ASA postulate in triangle congruence?

Back

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

Front

What is the significance of corresponding parts in congruent triangles?

Back

Corresponding parts in congruent triangles are significant because they allow us to conclude that if two triangles are congruent, then all their corresponding sides and angles are also congruent.