## Geometry Tutorial

#### Intro

In geometry, the parallelogram and the trapezoid are the fundamental quadrilaterals respectively to classify their own type. The types of parallelograms are the rectangle, rhombus, and square. The types of the trapezoid are the isosceles trapezoid and a right trapezoid.

#### Sample Problem

What are the properties of a parallelogram, a rectangle, a rhombus, a trapezoid and its types, and a square?

#### Solution

Properties of a Parallelogram:
1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. A diagonal divides it into 2 congruent triangles.
4. Diagonals bisect each other.
5. Both pairs of opposite angles are congruent.
6. Consecutive angles are supplementary.

Properties of a Rectangle:
1. All the properties of a parallelogram.
2. Has a right angle.
3. Diagonals are congruent.

Properties of a Rhombus:
1. All the properties of a parallelogram.
2. All sides are congruent.
3. Diagonals are perpendicular.
4. Diagonals bisect the opposite angles.

Properties of a Square:
1. All the properties of a parallelogram.
2. All the properties of a rectangle.
3. All the properties of a rhombus.

Properties of a Trapezoid:
1. Exactly one pair of opposite sides are parallel.

Properties of an Isosceles Trapezoid:
1. All the properties of a trapezoid.
2. Non-parallel sides are congruent.
3. Diagonals are congruent.

Properties of a Right Trapezoid:
1. All the properties of a trapezoid.
2. Has a right angle.