Congruent Triangles

Front

What is a congruent triangle?

Back

A congruent triangle is a triangle that has the same size and shape as another triangle, meaning all corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' represents congruence, indicating that two figures have the same shape and size.

Front

What are the three main criteria for triangle congruence?

Back

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

Front

What does the SSS postulate state?

Back

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

Front

What does the SAS postulate state?

Back

The SAS 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 two triangles are congruent.

Front

What does the ASA postulate state?

Back

The ASA 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 two triangles are congruent.

Front

What is the value of z in triangle congruence problems?

Back

The value of z often represents a variable in equations derived from the properties of congruent triangles, which can be solved using algebra.

Front

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

Back

Two triangles can be determined to be congruent if all three corresponding angles are equal, which is known as the Angle-Angle-Angle (AAA) criterion.

Front

What is the significance of the congruency statement ∆UST ≅ ∆MKL?

Back

The congruency statement ∆UST ≅ ∆MKL indicates that triangle UST is congruent to triangle MKL, meaning all corresponding sides and angles are equal.

Front

What is the length of segment BM if it is given in a congruence problem?

Back

The length of segment BM can be determined using the properties of congruent triangles, often involving the use of given measurements or algebraic expressions.