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?

Answer 1

Answer

Statement 3: The side BC = BC (common side for ΔADC and ΔBCD)

Solution

Rectangle ABCD having diagonals AC and DB:  

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: The side BC = BC (common side for ΔADC and ΔBCD)

Statement 4: Triangle ADC and BCD are congruent (by SAS postulate) Statement 5: AC = BD (by CPCTC)

The statement 3 completes Jimmy's proof.

Answer 2

Answer:

Statement 3: DC=CD (Common)

Step-by-step explanation:

According from the  statement given, consider ΔADC and ΔBCD, we get

AD=BC(opposite sides of a rectangle are congruent)

∠ADC=∠BCD(angles of a rectangle are 90°)

DC=CD(Common)

Thus, by SAS rule, ΔADC≅ΔBCD and by CPCTC AC=BD.

Thus, Statement 3 that is using the common sides of the triangle jimmy can prove the proof.