Does every trapezoid have 2 pairs of opposite parallel sides

Posted By Admin @ September 03, 2022

Question:

Which statement about a quadrilateral is true?

All trapezoids have two pairs of parallel sides.
Only some rectangles have four right angles.
All squares are rectangles.
Some rhombuses are trapezoids.

Answer:

The statement "All squares are rectangles" is true and all the other statements are false according to the properties of quadrilaterals.

What are the properties of quadrilaterals?

A quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°.

The quadrilaterals are of many types based on their properties.

Properties:

  • Rectangle: All the angles in a rectangle are right angles. Thus, all angles in a rectangle are equal.
  • Square: All the sides are equal and angles are also equal. Just like a rectangle, a square has four right angles.
  • Rhombus: All sides are equal in length and opposite sides are parallel to each other.
  • Trapezoid: Has only one pair of parallel sides and those are called the bases of the trapezoid. The other two sides are called legs or lateral sides.

Verifying the given statements:

Option A: "All trapezoids have two pairs of parallel sides" - False.

  • From the properties, it is known that every trapezoid has only one pair of parallel sides and are called the bases of the trapezoid.

Option B: "Only some rectangles have four right angles" - False

  • From the properties, it is known that all the angles in a rectangle must and should be equal and are 90° each.

Option C: "All squares are rectangles" - True

  • From the properties, like a rectangle, a square has four right angles. So, the statement is true.

Option D: "Some rhombuses are trapezoids" - False

  • From the properties, all sides in a rhombus are equal in length and opposite sides are parallel to each other. But in a trapezoid, there is only one pair of parallel sides.

Therefore, Option C "All squares are rectangles" is true.

Learn more about the properties of the trapezoid here:

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