Question

The figure below shows a rectangle ABCD having diagonals AC and DB: A rectangle ABCD is shown with diagonals AC and BD. Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Jimmy's proof: Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent) Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°) Statement 3: Statement 4: Triangle ADC and BCD are congruent (by SAS postulate) Statement 5: AC = BD (by CPCTC) Which statement below completes Jimmy's proof? AB=AB (reflexive property of equality) AB=AB (transitive property of equality) DC=DC (reflexive property of equality) DC=DC (transitive property of equality)

Answer 1

Answer: DC=DC (reflexive property of equality)

Step-by-step explanation:

The reflexive property of equality states that a value is equal to itself.

Given: ABCD is a rectangle,

Where AB, BC, CD, and DA are the sides of the rectangle while AC and BD are the diagonals of the rectangle. ( Shown in below diagram)

To prove: The diagonals of ABCD are congruent.

That is, $AC = BD$

Proof:  In triangles ADC and BCD,

$AD = BC$   ( Opposite sides of a rectangle are congruent )

$\angle ADC = \angle BCD$  ( Angles of a rectangle are of 90° )

$DC = DC$                 ( Reflexive property of equality )  

Thus, By SAS postulate of congruence,

$\triangle ADC\cong \triangle BCD$

By CPCTC,

$AC = BD$        

⇒ The diagonals of rectangle are congruent.