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For each of the following quadrilaterals, select all the properties that must be true.All sides congruent Four right angles Two pairs of parallel sides Only one pair of parallel sides(a) Rectangle (b) Trapezoid (c) Parallelogram

Question

For each of the following quadrilaterals, select all the properties that must be true.All sides congruent Four right angles Two pairs of parallel sides Only one pair of parallel sides(a) Rectangle (b) Trapezoid (c) Parallelogram

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Solution

(a) Rectangle:

  • All sides are not necessarily congruent. This is only true for a square, which is a specific type of rectangle.
  • Four right angles. This is a defining characteristic of a rectangle.
  • Two pairs of parallel sides. This is also a defining characteristic of a rectangle.
  • Only one pair of parallel sides. This is not true for a rectangle, as it has two pairs of parallel sides.

(b) Trapezoid:

  • All sides congruent. This is not necessarily true for a trapezoid.
  • Four right angles. This is not true for a trapezoid.
  • Two pairs of parallel sides. This is not true for a trapezoid, as it only has one pair of parallel sides.
  • Only one pair of parallel sides. This is a defining characteristic of a trapezoid.

(c) Parallelogram:

  • All sides congruent. This is not necessarily true for a parallelogram. This is only true for a rhombus, which is a specific type of parallelogram.
  • Four right angles. This is not necessarily true for a parallelogram. This is only true for a rectangle, which is a specific type of parallelogram.
  • Two pairs of parallel sides. This is a defining characteristic of a parallelogram.
  • Only one pair of parallel sides. This is not true for a parallelogram, as it has two pairs of parallel sides.

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