The figure below shows rectangle ABCD with diagonals segment AC and segment BD:

Question

Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent:

Zinnia's proof:

Statement 1: Rectangle ABCD is given

Statement 2:  ≅  because opposite sides of a rectangle are congruent

Statement 3:  ≅  by the reflexive property of congruence

Statement 4: Angles ADC and BCD are both right angles by definition of a rectangle

Statement 5: Angles ADC and BCD are congruent because all right angles are congruent

Statement 6:

Statement 7:  ≅  by CPCTC

Which statement below completes Zinnia's proof?

 Triangles ADC and BCD are congruent (by ASA postulate)

 Triangles ADC and BCD are congruent (by SAS postulate) 

Triangles ADC and CBA are congruent (by ASA postulate)

 Triangles ADC and CBA are congruent (by SAS postulate)

Answer 1

Hi Sally!

Choice number 2 is correct.

2 sides and the included angle

for both triangles. AD congruent

to BC, DC congruent to DC, and

the included right angles ADC

and BCD are congruent. This is

congruence by SAS for triangles

ADC and BCD.