The problem asks to classify quadrilaterals as trapezoids, isosceles trapezoids, or kites, based on their properties. The available properties are: - The legs are congruent. - The quadrilateral has four sides. - The quadrilateral has exactly one pair of parallel sides. - The quadrilateral has exactly two pairs of consecutive congruent sides with the opposite sides not congruent.
2025/3/13
1. Problem Description
The problem asks to classify quadrilaterals as trapezoids, isosceles trapezoids, or kites, based on their properties. The available properties are:
- The legs are congruent.
- The quadrilateral has four sides.
- The quadrilateral has exactly one pair of parallel sides.
- The quadrilateral has exactly two pairs of consecutive congruent sides with the opposite sides not congruent.
2. Solution Steps
First, let's review the definitions of each quadrilateral.
- Trapezoid: A quadrilateral with exactly one pair of parallel sides.
- Isosceles Trapezoid: A trapezoid whose non-parallel sides (legs) are congruent.
- Kite: A quadrilateral with two pairs of consecutive congruent sides such that opposite sides are not congruent.
- All quadrilaterals have four sides.
Now, let's classify the properties:
- Trapezoid: The defining property of a trapezoid is that it has exactly one pair of parallel sides. All quadrilaterals, including trapezoids, isosceles trapezoids, and kites, have four sides.
- Isosceles Trapezoid: An isosceles trapezoid has the properties of a trapezoid (exactly one pair of parallel sides and four sides) and an additional property that its legs are congruent.
- Kite: A kite is defined as a quadrilateral with exactly two pairs of consecutive congruent sides with the opposite sides not congruent. All kites have four sides.
Therefore, the assignments are as follows:
- Trapezoid:
- The quadrilateral has four sides.
- The quadrilateral has exactly one pair of parallel sides.
- Isosceles Trapezoid:
- The quadrilateral has four sides.
- The quadrilateral has exactly one pair of parallel sides.
- The legs are congruent.
- Kite:
- The quadrilateral has four sides.
- The quadrilateral has exactly two pairs of consecutive congruent sides with the opposite sides not congruent.
3. Final Answer
- Trapezoid: The quadrilateral has four sides, The quadrilateral has exactly one pair of parallel sides.
- Isosceles Trapezoid: The quadrilateral has four sides, The quadrilateral has exactly one pair of parallel sides, The legs are congruent.
- Kite: The quadrilateral has four sides, The quadrilateral has exactly two pairs of consecutive congruent sides with the opposite sides not congruent.