Reasoning and Proof Geometry Review

If M is the midpoint of AB, then AM=MB

• definition of angle bisector

• angle bisector theorem

• definition of midpoint

• midpoint theorem

If Y is between X and Z, the XY+YZ = XZ

• angle addition postulate

• segment addition postulate

• addition property

• definition of midpoint

If something is an angle, then it is acute. What is an appropriate counterexample?

• 70⁰

• 45⁰

• 120⁰

• True. There is no counterexample.

Tell whether the following is always, sometimes, or never true:

If line m lies in plane X and line m contains a point Q, then point Q lies in plane X.

• always

• sometimes

• never

Either draw a valid conclusion or state "no valid conclusion". If there is a valid conclusion, tell whether the conclusion is by the law of detachment or syllogism: Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram. The diagonals of quadrilateral PQRS bisect each other.

• No valid conclusion

• PQRS is a parallelogram, by Law of Detachment

• PQRS is a parallelogram by Law of Syllogism

Why are these 2 triangles congruent, based on your proof?

• ASA

• SAS

• SSS

• Hypotenuse Leg Thm

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

• Alternate Exterior Angle are Congruent

• Reflexive Property of Congruence

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

In the given proof, what is the statement for step 4?

What missing piece of information is needed to prove the triangles congruent using SAS?

• NM = AM

• NL = CA

• ∠M≅∠B

• ∠N≅∠C

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• Yes by ASA

• Yes by AAS

• Yes by SSA

• Not congruent