Geometric shapes

A triangle is a geometric shape with $3$ sides. In every triangle, the sum of angles equals $180$.
Below are the different types of triangles –

• Equilateral triangle - a triangle in which all sides are equal, all angles are equal, and every height is also a median and an angle bisector.
• Isosceles triangle - a triangle in which two legs are equal, two base angles are equal, and the median to the base is also the height and the vertex angle bisector.
• Right triangle - a triangle with one angle of $90$ degrees formed by two legs. The side opposite to the right angle is called the hypotenuse.
• Scalene triangle - a triangle in which all sides are different from each other.

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A rectangle is a quadrilateral with two pairs of parallel opposite sides.
It can also be defined as a parallelogram with a $90$ degree angle.
Since a rectangle is a type of parallelogram, it has all the properties of a parallelogram.

Here are the properties of a rectangle:

• Every pair of opposite sides are equal and parallel.
• All angles in a rectangle are equal to $90$ degrees.
• The diagonals of a rectangle are equal to each other.
• The diagonals of a rectangle bisect each other (divide each other in half, not just intersect).
• Since both diagonals are equal, all halves of the diagonals are equal.
• The diagonals of a rectangle are not perpendicular to each other and do not bisect the angles of the rectangle.

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A general trapezoid is a trapezoid where two of its opposite sides are parallel and are called the bases of the trapezoid.
The other two sides are called the legs of the trapezoid, and they are not parallel and face different directions.

Meet the basic properties of a trapezoid:

• Two sides are parallel to each other
• The sum of the angles that lean on the same leg (one from the small base and the other from the large base) is $180$ degrees.
• If we draw a diagonal that intersects both bases, it will create equal alternate angles between parallel lines.
• The sum of all angles in a trapezoid equals $360$ degrees.
• If we draw a segment that passes exactly through the middle of the $2$ legs of the trapezoid, we obtain a segment that is parallel to the bases and equal to half their sum.

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A parallelogram is a quadrilateral with $2$ pairs of parallel sides.
How to prove a parallelogram:

• First way:
  If in a quadrilateral every pair of opposite sides are parallel to each other, the quadrilateral is a parallelogram.
• Second way:
  If in a quadrilateral every pair of opposite sides are equal to each other, the quadrilateral is a parallelogram.
• Third way:
  If in a quadrilateral there is one pair of opposite sides that are both equal and parallel, the quadrilateral is a parallelogram.
• Fourth way:
  If in a quadrilateral, the diagonals bisect each other, the quadrilateral is a parallelogram.
• Fifth way:
  If in a quadrilateral there are two pairs of equal opposite angles, the quadrilateral is a parallelogram.

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A kite is a quadrilateral with two pairs of adjacent equal sides.
To better understand this, imagine that a kite is composed of two isosceles triangles joined together.

Here are the main properties of the kite:
The main diagonal in a kite, which extends from the two vertices of the triangles, is both an angle bisector, a median, and perpendicular to the secondary diagonal, which extends from the base angles of the triangles.
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A rhombus is a parallelogram with a pair of adjacent sides that are equal.
Here are the properties of a rhombus:

• In a rhombus, all sides are equal.
• In a rhombus, there are two pairs of parallel opposite sides.
• In a rhombus, adjacent angles sum to $180$ degrees.
• The sum of angles is $360$ degrees.
• In a rhombus, there are two pairs of equal opposite angles.

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