Question

Trapezoid ABCD has vertices A(2,4) B(5,4) C(7,1) D(0,1)

Is this trapezoid an isosceles trapezoid?

Answer 1

Answer: Yes, ABCD is isosceles trapezoid.

Explanation:

Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.

In trapezoid ABCD sides are AB, BC, CD and DA.

According to the question, A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)

After making the diagram of ABCD, we found that DA and BC are nonparallel sides.

And, by the distance formula
`BC=√((7-5)^2+(1-4)^2)`

⇒
`BC=√(4+9)`=
`√(13)`

⇒
`BC=√(13)` unit.

Similarly,
`DA=√((2-0)^2+(4-1)^2)`

⇒
`DA=√(13)` unit.

Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.

Therefore, trapezoid ABCD is a isosceles trapezoid.

Answer 2

Yes

Explanation:

Segments AB and CD are parallel and 3 units apart.

Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.