Question

Use two 2-Column proofs to show that either diagonal of a rectangle will create two congruent triangles?

Answer 1

Given: Rectangle ABCD 
Prove: ∆ABD≅∆CBD 
Solution:
                      
            Statement                                       Reason 

  ABCD is a parallelogram          Rectangles are parallelograms since the                                                          definition of a parallelogram is a quadrilateral                                                    with two pairs of parallel sides.

Segment AD = Segment BC       The opposite sides of a parallelogram are     Segment AB = Segment CD       congruent. This is a theorem about the                                                              parallelograms.

∆ABD≅∆CBD                             SSS postulate: three sides of ΔABD is                                                           equal to the three sides of ∆CBD


Given: Rectangle ABCD 
Prove: ∆ABC≅∆ADC
Solution:
                      
            Statement                                       Reason 

    Angle A and Angle C                 Definition of a rectangle: A quadrilateral     
        are right angles                      with four right angles.

        Angle A = Angle C                 Since both are right angles, they are                                                                  congruent

Segment AB = Segment DC       The opposite sides of a parallelogram are     Segment AD = Segment BC       congruent. This is a theorem about the                                                              parallelograms.

            ∆ABC≅∆ADC                   SAS postulate: two sides and included                                                         angle of ΔABC is congruent to the two                                                         sides and included angle of ∆CBD