Geometry - Lessson 4.2

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

If \( \Delta GAM \cong \Delta ERS \), what can be inferred about their corresponding angles?

Back

The corresponding angles of congruent triangles are equal. Therefore, \( m\angle GAM = m\angle ERS \), \( m\angle AGM = m\angle RES \), and \( m\angle GMA = m\angle SER \).

Front

What is the Angle-Angle (AA) criterion for triangle congruence?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are congruent.

Front

What is the Side-Side-Side (SSS) criterion for triangle congruence?

Back

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

Front

What is the Side-Angle-Side (SAS) criterion for triangle congruence?

Back

The SAS criterion 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

If \( GA = 11 \), \( GM = 8 \), and \( AM = 7 \) in \( \Delta GAM \), what is the perimeter of the triangle?

Back

The perimeter of \( \Delta GAM \) is \( GA + GM + AM = 11 + 8 + 7 = 26 \).

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in a triangle is always \( 180\degree \).

Front

If \( m\angle S = 97\degree \) and \( m\angle T = 43\degree \) in \( \Delta STA \), what is \( m\angle A \)?

Back

Using the angle sum property, \( m\angle A = 180\degree - (m\angle S + m\angle T) = 180\degree - (97\degree + 43\degree) = 40\degree \).

Front

What is the definition of corresponding sides in congruent triangles?

Back

Corresponding sides in congruent triangles are the sides that are in the same relative position in each triangle.

Front

What is the significance of the notation \( \Delta \)?

Back

The notation \( \Delta \) is used to denote a triangle in geometry.