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Quadrilaterals
Concept
In geometry, a quadrilateral is a closed shape that is formed by joining four points among which any three points are non-collinear. A quadrilateral has 4 sides, 4 angles, and 4 vertices. ‘Quadrilateral’ is derived from a Latin word, in which, ‘Quadra’ means four and ‘Latus’ means sides. All 4 sides of a quadrilateral may or may not be equal.
Although a quadrilateral always has four sides, four angles, and four vertices, the measure of the sides and angles differ. It is to be noted that the sum of the interior angles of a quadrilateral is always equal to 360°. Below are the different types of quadrilaterals.
Rules
A square is a quadrilateral because it has 4 sides. It is also a parallelogram because opposite sides are parallel. It is a special rectangle with 4 right angles and 4 congruent sides.
A rhombus is a quadrilateral because it has 4 sides. It is also a parallelogram because opposite sides are congruent. However, it is not a rectangle because it does not have 4 right angles. Instead, it has 2 acute and 2 obtuse angles.
A trapezoid is a quadrilateral because it has 4 sides. However, it is not a parallelogram because two of its sides are not parallel. It is also not a rectangle, because it does not always have right angles. Instead, it has 2 acute and 2 obtuse angles and one pair of parallel sides.
Example
Solution
Yes, all squares are rhombuses as a square is a quadrilateral with 4 equal-length sides and opposite sides parallel to each other just like a rhombus.
Practice Quadrilaterals
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Quadrilateral – a 4-sided figure.
Parallelogram – a 4-sided figure with opposite sides parallel.
Rectangle – a figure with 4 straight sides and 4 right angles.
Square – a figure with 4 equal straight sides and 4 right angles.
Rhombus – a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and 4 equal sides.
Trapezoid – a quadrilateral with only one pair of parallel sides.
Parallel – lines that run alongside one another without intersecting.
Congruent – having the same size and shape.
Right angles – angles that are 90°.
Acute angles – angles that are less than 90°.
Obtuse angles – angles that are more than 90°.