Intro to Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the symbol used to denote congruence in geometry?

Back

The symbol for congruence is '≅'.

Front

If \( \Delta ABC \cong \Delta DEF \), what can we say about their corresponding angles and sides?

Back

The corresponding angles and sides of the triangles are equal: \( \angle A = \angle D, \angle B = \angle E, \angle C = \angle F \) and \( AB = DE, BC = EF, AC = DF \).

Front

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

Back

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

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

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

Back

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

If \( \angle A = 48^\circ \) in \( \Delta ABC \) and \( \Delta DEF \) is congruent to \( \Delta ABC \), what is \( \angle D \)?

Back

\( \angle D = 48^\circ \) because corresponding angles in congruent triangles are equal.

Front

How do you denote the congruence of triangles in a statement?

Back

You denote the congruence of triangles by writing the triangle names in order of their corresponding vertices, e.g., \( \Delta ABC \cong \Delta DEF \).

Front

What is the importance of the order of vertices in triangle congruence?

Back

The order of vertices is important because it indicates which angles and sides correspond to each other.