Segment and Angle Proof Properties

If AB=CD then AB+EF = CD + EF.

• Division property of equality
• Addition Property of equalilty
• Transitive property of equality
• Substitution

QR=QR

• Reflexive property of equality
• Symmetric property of equality
• Subtraction property of equality
• Transitive property of equality

If RS+TU=XY and TU=WV, then RS + WV=XY.

• Segment Addition Postulate
• Addition of Equals
• Substitution
• Division of equals

If JK equals LM, then line segment JK is congruent to line segment LM.

• Definition of midpoint
• Transitive Property
• Symmetric Property
• Definition of Congruence

If AB=BC and BC=CE then AB=CE.

• Transitive property
• Multiplication of equality
• Reflective property of equality
• Distributive property of equality

If 2XY=YZ, then XY = 1/2 YZ.

• Multiplication of equality
• Division of equality
• Subtraction of equality
• Midpoint

If Q is between P and R, then PQ +QR=PR.

• Segment Addition postulate
• Definition of Midpoint
• Addition Property of equality
• Transitive Property

If 2KL=KL + MN then KL=MN.

• Segment addition postuate
• Definition of Midpoint
• Subtraction of equality
• Division of equality

Give the reason for statement 1.

• Given
• Angle addition postulate
• Segment Addition Postulate
• Complementary Angles

Give the reason for statement #3

• Definition of complementary angles
• Angle addition postulate
• Definition of supplementary angles
• Substitution of equalities