Illustrated · 2 min
A parallelogram is a four-sided plane rectilinear figure with opposite sides parallel. This means that opposite angles are equal, opposites sides are equal, and diagonals bisect. Here is a diagram of a parallelogram. The green and red angles are equal, and the equal sides are represented by tick marks. There are no lines of symmetry. The perimeter is 2(a+b) when b is a base, and a is a side. The area is hb when h is the height and b is a base.
A kite is a geometric shape that has two pairs of equal sides, and each pair of equal sides are adjacent. The angles are equal where each pair of non-congruent sides meet. The diagonals not only meet at right angles (that is, they are perpendicular to each other), but also, one diagonal bisects the other. There is one line of symmetry. The perimeter of a kite is 2(a+b) as well, where a is the shorter side, and b is the longer side. The area is pq/2.
An isosceles trapezoid is a a cyclic quadrilateral with equal diagonals or a cyclic quadrilateral with a pair of parallel sides. Their adjacent angles are either equal to them or supplementary. Their diagonals are equal in length. There is one line of symmetry. The perimeter of one is 2(a+b1+b2) where a is a side length, and b1 and b2 are base lengths. The area is 1/2(b1+b2)h, where h is the height and b1 and b2 are the bases. Here is a diagram of a isosceles trapezoid.
A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides. There are two lines of symmetry (dashed lines). The perimeter of a rhombus is 4s, where s is a side length. The area of a rhombus is pq/2, where p and q are lengths of diagonals. Here is a diagram of a rhombus.
A rectangle is a parallelogram with right angles. This means that all its angles are 90 degrees, their diagonals bisect and are of equal length, and their two pairs of sides are parallel. A rectangle is a cyclic quadrilateral - that is, every one of its points would fit on the edge of a circle. The radius of that circle would be half of a diagonal. The perimeter of a rectangle is 2w + 2l where l is the length and w is the width. The area of a rectangle is lw where l is the length and w is the width. Here is a diagram of a rectangle.
A square is a plane figure with four equal straight sides and four right angles. It has four lines of symmetry, and diagonals bisect and are equal. The perimeter is 4s where s is a side, and the area is s^2. Here is a diagram of a square.
Special quadrilaterals as a whole are pretty cool shapes!
~ Abigale Kim (a+bi)