Write A Two Column Proof

Question

Given: Segment AC ≅ Segment BC
Prove: ∠A ≅ ∠B

Answer 1

 

Given triangle ABC is isosceles;

Prove: base angles are congurent

 

Statement                                           Reason

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Isosceles triangle                              given

 

Drops the perpendicular height        perpendicular height can be constructed from the (external) top point

                                                     of the triangle to the base; Labels the intersection of the height and the base M.

 

AB = AC                                        given; isosceles triangles have two sides that are congruent

 

AM = AM                                        reflexive

 

Triangles ABM and ACM

are congruent right triangles            HL

 

Base angles are congruent         CPCTC