Proofs in Geometry

In the given proof, what is the statement for step 2?

By what reasoning are the two triangles congruent?

• SSS

• SAS

• ASA

• The triangles are not congruent.

Are the triangles congruent, if yes, why?

• SSS

• SAS

• ASA

• Not Congruent

In the given proof, what is the reason for final step?

• Reflexive Property of Congruence

• Corresponding Parts of Congruent Triangles are Congruent

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

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

What should you conclude by definition of perpendicular?

• <ORP is a right angle

• QR + RP = QP

• <ORQ and <ORP are complementary

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 supplementary. What can you conclude?

• m<1 + m<2 = 180

• m<1 + m<2 = 90

• m<1 = m<2

• nothing

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