Chapter Closure
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B: Kite, see solution.
C: Rectangle, see solution.
D: Trapezoid, see solution.
Investigating the shapes in terms of these characteristics, we can classify them.
From the diagram, we see that the given shape has four vertices. Also, no lines are of equal length or parallel, which makes this shape a quadrilateral.
Shape B also has four vertices. We also see that it has two pairs of sides with equal lengths. This fits the description of a kite.
Again, like with the previous shapes, the shape has four vertices. However, we also know that all of its angles are right angles. This is called a rectangle. Note that a rectangle has, by definition, two pairs of parallel sides.
The last shape also has four vertices. From the diagram we also see that it has one pair of parallel sides, which means this is a trapezoid.
If a shape has reflection symmetry, we can fold the shape over itself using the line of reflection as crease. Examining the shape, we cannot identify any line of reflection. Also, there are no markings telling us that any of the sides are parallel. Therefore, Shape A should be placed outside of the circles.
The first thing we can say about a kite is that it does not have any parallel sides. However, it does have one line of reflection.
Therefore, this shape should be placed in the left circle, but not in the right.
The definition of a rectangle is a quadrilateral with four right angles and two pairs of parallel sides. Therefore, the shape should definitely be inside the right circle. Also, a rectangle has two lines of symmetry — one through the midpoints of each pair of parallel sides.
Therefore, Shape C should be placed in the intersection of the two circles.
If the trapezoid was an isosceles trapezoid, we would have one line of symmetry. However, since this is not the case, it does not have any line of symmetry. This places it outside of the left circle. A trapezoid is defined as a quadrilateral with one pair of parallel sides. With this information, we can place the shape correctly in the diagram.
