Triangle Congruence Proofs

Front

What is the Hypotenuse-Leg (HL) theorem in triangle congruence?

Back

The HL theorem states that if a right triangle has a hypotenuse and one leg that are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What must be stated when using the HL theorem in a proof?

Back

It must be stated that there are right triangles.

Front

What does AB∥DC indicate in a triangle proof?

Back

AB∥DC indicates that line segments AB and DC are parallel.

Front

What is the significance of alternate interior angles in triangle proofs?

Back

Alternate interior angles are congruent when two parallel lines are cut by a transversal, which can be used to prove triangle congruence.

Front

What does FH≅FH represent in a proof?

Back

FH≅FH represents the reflexive property, stating that a segment is congruent to itself.

Front

What is the purpose of stating HD=DN in a proof?

Back

Stating HD=DN establishes that two segments are equal, which is necessary for proving triangle congruence.

Front

What are the three main criteria for triangle congruence?

Back

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

Front

What is the Angle-Angle-Angle (AAA) criterion in triangle congruence?

Back

The AAA criterion states that if two triangles have all three angles congruent, they are similar, but not necessarily congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are identical in size and shape, while similarity means they have the same shape but may differ in size.

Front

What role does the transitive property play in triangle congruence?

Back

The transitive property states that if two triangles are congruent to a third triangle, then they are congruent to each other.