5. Properties of Trapezoids and Kites
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Recall the classification of quadrilaterals.
Quadrilateral, see solution.
We are given the following diagram and asked to given the most specific name for this quadrilateral.
Let's recall the definitions of different types of quadrilaterals.
Quadrilateral | Definition |
---|---|
Parallelogram | Both pairs of opposite sides are parallel. |
Rhombus | Parallelogram with four congruent sides. |
Rectangle | Parallelogram with four right angles. |
Square | Parallelogram with four congruent sides and four right angles. |
Trapezoid | Quadrilateral with exactly one pair of parallel sides. |
Isosceles Trapezoid | Trapezoid with legs that are congruent. |
Kite | Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent. |
Now, we can go through each of them and see whether our quadrilateral meets the description.
Quadrilateral | Does CDEF meet the definition? | Reasoning |
---|---|---|
Parallelogram | No | The opposite sides are not marked as parallel. |
Rhombus | No | There are only two congruent sides, not four. |
Rectangle | No | The angles seem to be right angles, but they are not marked as such. |
Square | No | Not all sides are congruent and the measures of the angles are unknown. |
Trapezoid | No | None of the sides are marked as parallel. |
Isosceles Trapezoid | No | It is not a trapezoid. |
Kite | No | One pair of opposite sides is congruent. |
As we can see, we do not have enough information to specify CDEF as some kind of quadrilateral. All we know for sure is that CDEF has four sides and four vertices, so the most specific name we can give it is a quadrilateral.