Chapter Closure
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What are the characteristics of the four quadrilaterals?
A. rectangle
B. rhombus
C. kite
D. trapezoid
Let's first go over the characteristics of the four quadrilaterals in the list.
A square is a quadrilateral with two pairs of parallel sides, four pairs of congruent sides and four right angles.
The shape of a square has the characteristics of both a rhombus and a rectangle. Therefore, if a shape is a square, then it is both a rhombus and a rectangle.
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If a shape is a square, then it must also be a rectangle. |
The only way the diagonals of a quadrilateral are perpendicular to each other is if the quadrilateral has four congruent sides. This is because the diagonals create isosceles triangles where the diagonals makes up the triangle's height.
The only quadrilateral that has four congruent sides is the rhombus.
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The diagonals of a rhombus must be perpendicular to each other. |
If a quadrilateral has a line of symmetry, we can fold it along that line such that the folded part lines up with the unfolded part. The rhombus and rectangle will always have two lines of symmetry. The kite and trapezoid however, will at most have one line of symmetry.
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If the quadrilateral has only one line of symmetry, then it could be a kite. |
According to the characteristics of the four shapes, the kite, rectangle and rhombus all have more than two sides that are congruent. Therefore, the only shape it could be is the trapezoid.
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If a quadrilateral has only two sides that are congruent, then the shape could be a trapezoid. |
With the given information, we can assign a quadrilateral to each statement so that we only use each quadrilateral name once. A.& rhombus or rectangle &&→ rectangle B.& rhombus &&→ rhombus C.& kite or trapezoid &&→ kite D.& trapezoid &&→ trapezoid