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A quadrilateral is a polygon with 4 sides. It can be concave, or convex, simple, or complex, regular, or irregular but it must always have 4 straight lines for sides.

Every quadrilateral has 4 sides (these are called edges), 4 corners (these are called vertices), and 4 angles.

The angles inside a quadrilateral always add up to 360°.

For example, in a rectangle, all 4 angles are 90° .

90° + 90° + 90° + 90° = 360°

This is also true for every quadrilateral, not just rectangles.

For example: In the quadrilateral given below, the measurements are:

Top left - 92°

Top right - 66°

Left -  128°

Bottom -  74°

Hence, the sum of the angles is: 92° + 66° + 128° + 74° = 360°

Every 4-sided figure is a quadrilateral, but there are some specific quadrilaterals.

Lets discuss them:

1. Parallelogram

A parallelogram has two pairs of parallel sides. (Parallel means the lines never cross – like railroad tracks). In a parallelogram, the sides across from each other are not only parallel but they are also the same size.

2. Rhombus

A rhombus is a parallelogram that has 4 equal sides. That may sounds like we’re describing a square, but as you can see, a rhombus isn’t necessarily a square. A rhombus typically looks like a square that is slanted.

3. Square

A square is a parallelogram with 4 equal sides and 4 right angles. (Remember right angles look like a perfect corner.)

4. Rectangle

A rectangle is a parallelogram with 4 right angles.

Notice that the definition of a rectangle doesn’t say anything about the length of the sides. That’s because not all the sides are equal. However, because it says it’s a parallelogram, that means the sides opposite of each other will be equal.

5. Trapezoid

A trapezoid has only one pair of parallel sides. Remember that a parallelogram had two pairs of parallel sides. In contrast, a trapezoid only has one pair. Also, there’s no guarantee that any of the sides are equal.

6.Kite

A kite has two pairs of equal sides, but the equal sides are right next to each other.

That’s different than a parallelogram, which has equal sides but they are across from each other. The diagonals of a kite (shown in the picture with dashed lines) always make a right angle.

Summary

Quadrilateral: A quadrilateral is a polygon with 4 sides.

Every 4-sided figure is a quadrilateral, but there are some specific quadrilaterals:

1. A parallelogram has 2 pairs of parallel sides.

2. A rhombus is a parallelogram that has 4 equal sides.

3. A square is a parallelogram with 4 equal sides and 4 right angles.

4. A rectangle is a parallelogram with 4 right angles.

5. A trapezoid has only one pair of parallel sides.

6. A kite has two pairs of equal sides, but the equal sides are right next to each other.

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