Geometry Proofs

Given: <1 and <3 are vertical angles. What should you conclude by the vertical angles theorem?

• <1 and <2 are a linear pair

• <1 and <3 are right angles

• <2 and <4 are vertical angles

Given: <1 and <2 are a linear pair. Conclusion: m<1 + m<2 = 180. What is the reason that allows you to draw that conclusion?

• Angle addition postulate

• Definition of straight angle

• Linear Pair Postulate

• Definition of supplementary

What is the missing statement in the proof?

• Addition property

• Segment Addition Postulate

• Substitution property

• Transitive property

Given: B is the midpoint of AC. What should you conclude?

• AB + BC = AC

• AB = BC

• A is the segment bisector of BC

• ABC is a straight angle

Fill in the blanks to complete the geometric proof:

• ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

How can you prove step #4?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

How can you prove step #5?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

What is the "reason" for step 5 of the proof?

• Angle Bisector Theorem

• Reflexive property

• CPCTC Theorem

• Proof

Identify the  missing statement or reason

• Given

• Vertical Angles Theorem

• Definition of Angle Bisector

• Alternate Interior Angles Theorem