Congruent Triangle Proofs

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

What does the Reflexive Property state in geometry?

Back

Front

List the triangle congruence criteria. What are they?

Back

The triangle congruence criteria are: 1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side) 5. HL (Hypotenuse-Leg for right triangles).

Front

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

Back

The SAS criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) congruence criterion?

Back

The AAS criterion states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the difference between ASA and AAS?

Back

ASA (Angle-Side-Angle) requires the included side between two angles to be congruent, while AAS (Angle-Angle-Side) does not require the side to be between the two angles.

Front

What is the SSA (Side-Side-Angle) condition? Is it a valid congruence criterion?

Back

The SSA condition is not a valid congruence criterion because it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the Midpoint Theorem?

Back

The Midpoint Theorem states that if a point is the midpoint of a segment, then it divides the segment into two equal parts.

Front

How can you prove that two triangles are congruent using the Reflexive Property?

Back

You can prove two triangles are congruent by showing that a side or angle in one triangle is congruent to the same side or angle in the other triangle, using the Reflexive Property.

Front

What is the significance of the 'given' statements in a triangle proof?

Back

The 'given' statements provide the initial conditions or information needed to start the proof process for triangle congruence.