MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

Answer:C. DC = DC. By reflexive property of equality.Step-by-step explanation:We are given that,In step 4, Jimmy proved ΔADC ≅ ΔBCD by the SAS Congruence Postulate.For that, the previous steps states,Step 1: AD = BC, as opposite sides of a rectangle are congruent.Step 2: ∠ADC = ∠BCDSo, in order to satisfy the SAS Postulate, we must have another pair of sides equal from the respective rectangles.As, we can see that in ΔADC and ΔBCD, the side DC is a common side.Thus, in the missing step, we get,Step 3: DC = DC, By the reflexive property of equality.Hence, option C is correct.