Question 6(Multiple Choice Worth 1 points)

(03.04 HC)

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)

Question

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Respuesta :

wagonbelleville wagonbelleville · Answer 1 · 2019-01-17T08:56:46+01:00

Answer:

3. DC = DC : Reflexive property of equality

Step-by-step explanation:

We are given that ΔADC ≅ ΔBCD by SAS postulate.

SAS postulate states that when two corresponding sides of triangles are equal with the included angles being equal, then the triangles are congruent.

Now, while stating that triangles are congruent, the positioning of letters is important.

As, we have that sides AD = BC and ∠ADC = ∠BCD.

Also, the diagonals AC = BD are proved.

Thus, we see that from ΔADC ≅ ΔBCD that sides DC = CD.

So, we get that DC = DC by the reflexive property of equality, which states that a value is equal to itself.

Hence, option 3 is correct.