There are countless different type of quadrilaterals, but all have actually several points in common: all of them have four sides, room coplanar, have actually two diagonals, and the sum of their 4 interior angles amounts to 360 degrees. This is exactly how they space alike, but what makes them different?

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We know many quadrilaterals through their distinct shapes and also properties, prefer squares. Remember, if girlfriend see the word quadrilateral, the does no necessarily typical a figure with distinct properties favor a square or rectangle! In indigenous problems, be careful not come assume the a quadrilateral has parallel sides or same sides uneven that is stated.

You are watching: Why is a quadrilateral only sometimes a parallelogram?

Special Quadrilaterals


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A parallelogram has actually two parallel bag of the contrary sides.

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A rectangle has actually two bag of opposite sides parallel, and also four ideal angles. The is likewise a parallelogram, because it has two bag of parallel sides.

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A square has two bag of parallel sides, 4 right angles, and also all four sides room equal. The is additionally a rectangle and also a parallelogram.

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A rhombus is characterized as a parallel with four equal sides. Is a rhombus always a rectangle? No, due to the fact that a rhombus go not need to have 4 right angles.
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Trapezoids only have one pair the parallel sides. It"s a type of quadrilateral the is no a parallelogram. (British name: Trapezium)

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Kites have 2 pairs of surrounding sides that space equal.

We deserve to use a Venn diagram to help us team the types of quadrilaterals.

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A Venn diagram offers overlapping one to show relationships in between groups that objects. Every "quadrilaterals" have the right to be separated into three sub-groups: basic quadrilaterals, parallelograms and trapezoids.

Is a rectangle constantly a rhombus? No, because all four sides that a rectangle don"t need to be equal. However, the sets of rectangles and also rhombuses execute intersect, and their intersection is the set of squares—all squares space both a rectangle and a rhombus.

We can put squares in the intersection the the 2 circles.

From this diagram, you can see that a square is a quadrilateral, a parallelogram, a rectangle, and also a rhombus!

Is a trapezoid a parallelogram? No, because a trapezoid has actually only one pair that parallel sides. The is why we must display the collection of trapezoids in a separate circle on the Venn diagram.

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What about kites? Kites room quadrilaterals the can it is in parallelograms. If their two pairs that sides are equal, it i do not care a rhombus, and if their angles are equal, it i do not care a square.

Related Links: Area formulas Perimeter formulas

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Homework aid | Geometry | Polygons
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·Polygon basics
·Triangles
·Quadrilaterals
·Area of polygon and also circles