9. LAT Triangle Congruence

Front

What does the congruence statement \( \Delta ABC \cong \Delta DEF \) imply about the angles?

Back

It implies that \( \angle A \cong \angle D \), \( \angle B \cong \angle E \), and \( \angle C \cong \angle F \).

Front

List the five ways to prove triangles congruent.

Back

SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), SAS (Side-Angle-Side), HL (Hypotenuse-Leg for right triangles).

Front

What is the first statement in the reason column of a proof?

Back

Given.

Front

What is the Vertical Angles Theorem?

Back

Vertical angles are congruent; if two angles are opposite each other when two lines intersect, they are equal.

Front

Define the Reflexive Property in geometry.

Back

For any geometric figure, it is congruent to itself; for example, \( AB \cong AB \).

Front

What is the significance of the Side-Angle-Side (SAS) congruence postulate?

Back

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Front

Explain the Angle-Side-Angle (ASA) congruence postulate.

Back

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Front

What does the Side-Side-Side (SSS) congruence postulate state?

Back

If all three sides of one triangle are congruent to all three sides of another triangle, the triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

In right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are congruent.

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape; all corresponding sides and angles are equal.