PROOFS

reflective property

The reflective property states that any geometric figure is congruent to itself. This property is fundamental in proving various geometric theorems.

symmetric property

The symmetric property states that if one geometric figure is congruent to another, then the second figure is also congruent to the first. This property is essential in establishing equality in geometric proofs.

transative property

The transitive property states that if one geometric figure is congruent to a second figure, and the second figure is congruent to a third figure, then the first and third figures are also congruent. This property is important for establishing relationships among multiple figures in geometric proofs.

substitution property

The substitution property states that if two geometric figures are congruent or have the same value, one can be substituted for the other in any equation or expression. This property is useful in simplifying proofs and calculations.

subtraction property

The subtraction property states that if two geometric figures are congruent, then subtracting the same quantity from both figures will maintain the congruence. This property is crucial for simplifying geometric proofs.

addition property

The addition property states that if two geometric figures are congruent, then adding the same quantity to both figures will maintain their congruence. This property is often used in geometric proofs and calculations.

linear pair postulate

The linear pair postulate states that if two angles form a linear pair, then they are supplementary, meaning their measures add up to 180 degrees. This postulate is essential in geometry for establishing relationships between angles.

Segment addition postulate

The segment addition postulate states that if point B is between points A and C on a line segment, then the length of segment AB plus the length of segment BC equals the length of segment AC. This postulate is fundamental in geometry for solving problems related to lengths of line segments.

vertical angle theorem

The vertical angle theorem states that when two lines intersect, the opposite (or vertical) angles formed are congruent. This theorem is frequently applied in geometric proofs and angle relationships.

Conngruent complements theorem

The congruent complements theorem states that if two angles are complements of the same angle (or congruent angles), then the two angles are congruent to each other. This theorem is often used in geometric proofs involving angle relationships.

congruent supplements theorem

The congruent supplements theorem states that if two angles are supplements of the same angle (or congruent angles), then the two angles are congruent to each other. This theorem is essential in geometric proofs involving angles.

Definition of right angles

Right angles are angles that measure exactly 90 degrees. They are commonly denoted by a small square at the vertex and play a crucial role in geometric proofs and constructions.

Inductive reasoning

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific instances or patterns observed. It is often used in mathematical proofs and problem-solving.

deductive reasoning

Deductive reasoning is a logical process where conclusions are reached based on previously established facts or premises. It is commonly employed in mathematical proofs to derive specific outcomes from general principles.