Question

Geometric proofs help?

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Which statement below completes Anastasia's proof?

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

Answer 1

You need a statement analogous to Statement 2 relating AD to BC. This allows the proof to proceed to Statement 3, using Pythagoras Theorem, to establish that \(AC^2=DB^2\).

So how are AD and BC related? Use the same rational as Statement 2.

Answer 2

Our lesson hasn't taught us how to use the Pythagorean Theorem yet, but I tried to figure it out prior to asking on here and I put D... I don't think it's right though.

Answer 3

Answer A is like the exact copy of Statement 2, right?

Answer 4

`opposite sides of a rectangle are parallel` isn't a proper justification of AD = BC

Answer 5

I only put that because our resource worksheet says that opposite sides of a rectangle are congruent and parallel for properties of rectangles, but I guess it doesn't really make sense.
So, if we have to use the same logic/rational as in Statement 2, would it be C?
sorry - I just really don't understand these.

Answer 6

yes it should be `AD = BC (opposite sides of a rectangle are congruent)`

Answer 7

it is true that the opposite sides of a rectangle are parallel

but that fact isn't useful in this case

Answer 8

Okay, thanks so much for helping make sense of this.

Answer 9

no problem