Question

for quadrilateral ABCD, determine the most precise name for it. A(2,3), B(12,3), C(8,6) and D(5,6). Show your work and explain.

Answer 1

ABCD is a trapezium. Since line AB and CD do not vary in y, they are parallel. Lines AD and BC are not parallel, as AD increases in x, and BC decreases in x. A quadrilateral with only one set of parallel lines is a trapezium.

Answer 2

1. Draw the points in the coordinate axes, as in the attached picture.

2. AB and CD are parallel, (both are parallel to the x-axis)

3. A is closer to the y axis than D and C is closer to the C closer than B

4. So combining 2 and 3, we conclude that ABCD is a trapezoid.

5. The remaining thing to check is whether the trapezoid is isosceles or not. For this we drop the heights to AB from points C and D,

and see that the distances from the feets of these heights to the points A and B are not equal.


Answer: Trapezoid