Geometry Proofs

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What is the Reflexive Property of Congruence?

Back

The Reflexive Property of Congruence states that any geometric figure is congruent to itself. For example, segment AB is congruent to segment AB.

Front

What is the significance of Corresponding Parts of Congruent Triangles are Congruent (CPCTC)?

Back

CPCTC is a theorem that states if two triangles are proven to be congruent, then their corresponding parts (sides and angles) are also congruent.

Front

How can you prove two triangles are congruent using the SAS criterion?

Back

To prove two triangles are congruent using SAS, you need to show that two sides of one triangle are congruent to two sides of another triangle, and the angle between those sides is also congruent.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the purpose of a proof in geometry?

Back

The purpose of a proof in geometry is to provide a logical argument that establishes the truth of a geometric statement or theorem based on previously established facts and definitions.

Front

What is the difference between a theorem and a postulate?

Back

A theorem is a statement that has been proven based on axioms and previously established theorems, while a postulate is a statement accepted as true without proof.

Front

What are the three main triangle congruence criteria?

Back

The three main triangle congruence criteria are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), and 3) Angle-Side-Angle (ASA).

Front

What does the term 'corresponding parts' refer to in triangle congruence?

Back

'Corresponding parts' refer to the sides and angles of two triangles that are in the same relative position. For example, if triangle ABC is congruent to triangle DEF, then angle A corresponds to angle D.

Front

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

Back

The ASA criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.