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.
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 [tex]BC=\sqrt{(7-5)^2+(1-4)^2}[/tex]
⇒[tex]BC=\sqrt{4+9}[/tex]=[tex]\sqrt{13}[/tex]
⇒[tex]BC=\sqrt{13}[/tex] unit.
Similarly, [tex]DA=\sqrt{(2-0)^2+(4-1)^2}[/tex]
⇒[tex]DA=\sqrt{13}[/tex] unit.
Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.
Therefore, trapezoid ABCD is a isosceles trapezoid.
