Proofs of Angles, Midsegments, and Medians

Question 1 In ∆ABC shown below, ∡BAC is congruent to ∡BCA. Given: Base ∡BAC and ∡ACB are congruent. Prove: ∆ABC is an isosceles triangle. When completed, the following paragraph proves that AB is congruent to BC making ∆ABC an isosceles triangle. Construct a perpendicular bisector from point B to .  Label the point of intersection between this perpendicular bisector and AD as point D.  m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.  ∡BDA is congruent to ∡BDC by the definition of congruent angles.  is congruent to DC by by the definition of a perpendicular bisector.  ∆BAD is congruent to ∆BCD by the _______1________.  AB is congruent to BC because _______2________.  Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

A:  1. corresponding parts of congruent triangles are congruent (CPCTC)  2. the definition of a perpendicular bisector

B:  1. the definition of a perpendicular bisector  2. the definition of congruent angles

C:  1. the definition of congruent angles  2. the definition of a perpendicular bisector

D: 1. the definition of congruent angles  2. corresponding parts of congruent triangles are congruent (CPCTC)

Use ∆ABC to answer the question that follows. Given: ∆ABC Prove: The three medians of ∆ABC intersect at a common point. When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point.

Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?

A  III, IV, II, I

B  IV, III, I, II

C  III, IV, I, II

D  IV, III, II, I

4: http://oi58.tinypic.com/hv9f5v.jpg

Question 5 (Multiple Choice Worth 4 points)

Triangle ABC is shown below. Given: ∆ABC  Prove: All three angles of ∆ABC add up to 180°. The flow chart with missing reason proves the measures of the interior angles of ∆ABC total 180°. Which reason can be used to fill in the numbered blank space?

A Alternate Exterior Angles Theorem

B Same-Side Interior Angles

C Corresponding Angles Postulate

D Alternate Interior Angles Theorem