"Given quadrilateral ABCD with A(0,0) B(4,2) C(3,3) and D(1,2), prove that ABCD is a non-isosceles trapezoid"
I don't understand how to put this as a proof, since I have to include formulas and reasons. Wouldn't a non-isosceles trapezoid be a normal trapezoid? Really lost..
yes, it is a "normal" trapezoid; it just means that its two non-parallel sides are not the same length. So, all you have to do is show that two of the sides of ABCD are parallel, and the others, not.
Clearly, AB and CD are parallel, since they have the same slope.
So, now you just have to show that AD≠BC
What you want to do is find the slope of all 4 sides and you should get to slopes the same...and follow a regular proof till you say its a trap.then to prove its not isosceles you use the for sides again but this time with the distance formula...and then you go along answering the proof
To prove that quadrilateral ABCD is a non-isosceles trapezoid, we need to show that it satisfies the definition of a trapezoid and that its two non-parallel sides are of different lengths.
Here is the step-by-step process to prove the claim:
1. Identify the coordinates of points A(0,0), B(4,2), C(3,3), and D(1,2) of quadrilateral ABCD.
- A(0,0), B(4,2), C(3,3), D(1,2)
2. Use the distance formula to find the lengths of each side of the quadrilateral.
- Length of AB: sqrt((4-0)^2 + (2-0)^2) = sqrt(16 + 4) = sqrt(20) = 2√5
- Length of BC: sqrt((3-4)^2 + (3-2)^2) = sqrt(1 + 1) = sqrt(2)
- Length of CD: sqrt((1-3)^2 + (2-3)^2) = sqrt(4 + 1) = sqrt(5)
- Length of DA: sqrt((0-1)^2 + (0-2)^2) = sqrt(1 + 4) = sqrt(5)
3. Observe that the lengths of the non-parallel sides AB and CD are different (2√5 ≠ sqrt(5)). Therefore, they are not equal, and the quadrilateral ABCD is not an isosceles trapezoid.
4. Confirm that the lengths of the parallel sides BC and AD are not relevant to determining if the quadrilateral is an isosceles trapezoid. However, you can find their lengths if desired.
By following these steps, you can prove that the quadrilateral ABCD is a non-isosceles trapezoid by showing that its non-parallel sides AB and CD have different lengths.