Question

The figure below shows a rectangle ABCD having diagonals AC and DB:

Answer 1

Statement
In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)

Answer 2

Answer:

Statement 4: $\Delta ADC\cong \Delta BCD$ (by SAS congruence).

Step by step explanation:

We have been given a rectangle and we are asked to find the missing statement to complete the Zinnia's proof.

Let us see how to prove that the diagonals of rectangle ABCD are congruent.

1. Since we know that opposite sides of rectangle are congruent. We can see that in triangle ADC and BCD, AD is opposite side of BC, therefore, AD=BC.  

2. Since we know that each angle of rectangle is equal to 90 degrees, therefore, $\angle ADC=\angle BCD$.

3. We can see that DC is base of both of our triangles. So, DC=DC by reflexive property of equality (something equals to itself).

4. We can see that both triangles, ADC and BCD, have two equal sides and an included right angle, therefore, by SAS congruence $\Delta ADC\cong \Delta BCD$.

5. Since we know that corresponding parts of congruent triangles are congruent, therefore, AC=BD.

Hence proven the diagonals of rectangle ABCD are congruent.