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.
2 answers:
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
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
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