Question

ABDC is an isosceles trapezoid. Given only the choices below, which properties would you use to prove ACD ≅ BDC by SSS?

The legs are congruent.
The base angles are congruent.
The bases are | |.
The diagonals are congruent.

(They all can be selected)

Answer 1

Answer: The legs are congruent.

The diagonals are congruent.

Explanation:

Given: ABDC is an isosceles trapezoid.

And we know that in isosceles trapezoid.

The legs and the diagonals are congruent. [property of isosceles trapezoid]

Thus, in
`\triangle{ACD}` and
`\triangle{BDC}`

`\overline{CD}=\overline{CD}....[\text{reflexive property}]`

`\overline{AC}=\overline{BD}..........[\text{ legs are congruent in isosceles trapezoid}]`

`\overline{AD}=\overline{BC}..........[\text{ diagonals are congruent in isosceles trapezoid}]`

`\Rightarrow\triangle{ACD}=\triangle{BDC}........[\text{SSS congruence postulate}]`

Answer 2

I think the correct answer would be the first option. To prove that ACD ≅ BDC by virtue of the SSS or side-side-side postulate, it should be that the answer is related with the sides of the trapezoid and the best option would be that the legs are congruent.