Basics of Proof

What is the justification (reason)?

• Reflexive

• A segment bisector divides a segment into 2 congruent segments

• A midpoint divides a segment into 2 equal segments

• Substitution

What is the reason?

• Perpendicular lines intersect to form right angles

• Vertical angles are congruent.

• All right angles are congruent

• An angle is formed by two rays sharing a common endpoint

What is the reason?

• An angle is formed by two rays sharing a common endpoint

• A segment bisector divides a segment into 2 congruent segments

• An angle bisector divides an angle into 2 congruent angles

• A midpoint divides a segment into 2 congruent segments

What is always the 1st statement in reason column of a proof?

• Prove
• Given
• Reason
• Statement

• An angle bisector divides an angle into 2 congruent angles

• Complements of congruent angles are congruent

• Perpendicular lines intersect to form right angles

• All right angles are congruent

• An angle bisector divides an angle into 2 congruent angles

• Vertical angles are congruent

• Congruent angles are congruent

• All right angles are congruent

• A midpoint divides a segment into 2 congruent segments

• A segment bisector bisector intersects a segment at its midpoint creating 2 congruent segments

• Substitution

• Reflexive

• Vertical angles are congruent

• All right angles are congruent

• An angle is formed by two rays sharing a common endpoint

• An angle bisector divides an angle into 2 congruent angles

• Perpendicular lines intersect to form right angles

• A segment bisector divides a segment into 2 congruent segments

• Substitution

• A midpoint divides a segment into 2 congruent segments

What reason supports the statement?

• Vertical angles are congruent.

• Parallel lines cut by a transversal form congruent alternate interior angles.

• Parallel lines cut by a transversal form congruent corresponding angles.

• Reflexive Property