Provide a two column proof for the following

Question

given: be bisects ad at c , ab ⊥ bc , de ⊥ ec , ab ≅ de prove: △ABC ≅ △DEC

Answer 1

Statement Reason

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BE bisects AD at C GIVEN

BC = CE defintion of Bisector

AB = DE GIVEN

Angle BCA = Angle ECD vertical angles are congruent

AB is perpendicular to BC GIVEN

DE is perpendicular to EC

angle ABC = DEC = 90 definition of perpendicular

angle BAC = angle EDC RUle for right triangle congruent

complements

AB^2 + BC^2 = AC^2; pythagorean

DE^2 + CE^2 = CD^2

AB^2 = DE^2; multiplication property of equality

BC^2 = CE^2;

AB^2 + BC^2 = DE^2 + CE^2 addition property of equality

AC^2 = CD^2 transitive/substitution

AC = CD square root of both sides

Triangles are def of congruent triangles: all 3 pairs of

congruent corresponding sides and all 3 pairs of

of corresponding angles are congruent

LL, SAS would be sufficient after step 7;

diagram uploaded to RESOURCES section under this link