Question

Trapezoid ABCD has vertices A(2, 4) , B(5, 4) , C(7, 1) , and D(0, 1) . Is this trapezoid an isosceles trapezoid?

Answer 1

Isosceles trapezoid

Explanation:

1)By definition, an isosceles trapezoid has two congruent sides and four vertices. According to the given coordinate points, what we have is an isosceles trapezoid. Graphically, we can say that:

`\overline{AD} \cong \overline BC`

2) Proving with Analytical Geometry that

`\overline{AD} \cong \overline BC`

`D_(BC)=\sqrt{(1-4)^(2)+(7-5)^(2)}\Rightarrow D_(BC)=√(9+4)\Rightarrow D_(BC)=√(13)\cong3.61\\D_(AD)=\sqrt{(1-4)^(2)+(0-2)^(2)}\Rightarrow D_(AD)=√(9+4)\Rightarrow D_(AD)=√(13)\cong3.61`

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.