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

Answer:

Isosceles trapezoid

Step-by-step 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

$\overline{AD} \cong \overline BC$

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

Answer 2

Answer:

Yes

Step-by-step 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.