Proofs and Transversals

What is the justification (reason)?

• reflexive property
• definition of segment bisect
• definition of a midpoint
• substitution property

If <1 and <2 are complementary, then m<1 + m<2 = 90

• Addition POE
• Subtraction POE
• Def of right angle
• Def of Complementary Angles

IF <ABC ≅ <DEF, then m<ABC = m<DEF

• Reflexive POE
• Addition POE
• Def. of congruent angles
• Def. of right angles

If X is between R & T on a line,
then RX + XT = RT

• Addition POE
• Substitution POE
• Angle Addition Post.
• Segment Addition Post.

What is the reason?

• Definition of Complementary
• Definition of 180 
• Definition of supplementary
• Angle Addition

Which property justifies the next step?

• Segment addition postulate
• Definition of an angle bisector
• Angle addition postulate
• Definition of right angles

Identify the  missing statement or reason

• Reflexive Property
• Definition of Midpoint
• Given
• Vertical Angles Theorem

Identify the  missing statement or reason

• Given
• Vertical Angles Theorem
• Definition of Angle Bisector
• Alternate Interior Angles Theorem

Identify the  missing statement or reason

• Definition of Angle Bisector
• Alternate Interior Angles Theorem
• Reflexive Property
• Definition of Midpoint

What is the "statement" for step 2 of the proof?

• ∆BAC≅∆DAC
• BC=DC
• ∡B≅∡D
• ∡BAC≅∡DAC