Lines, Figures, and Quadrilaterals
As review, a line is a straight, one dimensional figure that continues forever in both directions. Multiple lines can have unique properties, and the three properties we will describe are intersecting, parallel, and perpendicular lines. Any line can be drawn between two points in space. If we label one point as A and the other point as B, the notation for the line drawn through A and B is AB with an overhead arrow.
Intersecting lines are lines that cross. The lines don't have to be drawn crossing each other; as long as they are not parallel, they will intersect.
Parallel lines are lines that never intersect. They are often indicated by arrows pointing in the same direction on lines.
When writing that two lines are parallel, suppose we have line AB and line CD. We indicate that they are parallel using "||".
Perpendicular lines intersect at a 90 degree/right angle. They are denoted by small square where the lines intersect.
The notation of perpendicular lines m and n are represented by an upside down "T".
Solid figures are figures that are three-dimensional, like any object you can pick up. In math there are a variety of solid figures, such as cubes, prisms, and spheres.
Imagine if you took a square and added on an infinite number of layers of squares. You would get a cube, where every face of the cube is a square. A cube has 6 faces, the flat sides, and each face meets other face forming en edge. Three faces meet up forming a corner called a vertex. The infinite "layers" serve as depth for a 3D figure.
Adding depth to a circle would result in a cylinder, and adding depth to a rectangle would give you a rectangular prism. A rectangular prism has almost the same properties as a cube (6 faces, 12 edges, and 8 vertices), but each face can be a rectangle or a square.
Other solid figures are present all around you as well. A cone can be an ice cream cone or a birthday hat. Pyramids can be found in Egypt. A sphere is any ball. You can create any solid figure by adding depth to any 2D shape.
A quadrilateral is a four-sided, two-dimensional figure. All quadrilaterals have 4 straight edges and 4 vertices.
A square is a quadrilateral with four sides of equal length. The segments opposite each other are parallel and next to each other are perpendicular. All four interior angles are 90 degrees.
A rectangle is a quadrilateral who's opposite sides are the same length. All squares are rectangles. All four interior angles are 90 degrees.
A parallelogram is a quadrilateral who's opposite sides are parallel to one another and have equal length. Opposite interior angles are equal. All squares and rectangles are parallelograms.
A rhombus is a type of parallelogram with four equal sides. Again, interior angles do not have to be right angles. Squares are a type of rhombus.
A trapezoid is a quadrilateral who's top and bottom edges are parallel, but do not have to be the same length. Interior angles next to each other are equal.
A kite is a quadrilateral who's diagonals intersect at a right angle. In other words, the diagonals are perpendicular. Pairs of edges have the same length. Squares and rhombuses are kites.
Many of these quadrilaterals can fit into the descriptions of other quadrilaterals. To the right is a quadrilateral flow chart that shows some quadrilaterals belonging in multiple categories.
The three main categories of quadrilaterals are kites, parallelograms, and trapezoids.
A rhombus is a kite and a parallelogram. A rectangle is a parallelogram. An isosceles trapezoid is one that has two opposite sides of the same length.
A square is a rhombus and a rectangle, so a square must be a kite and parallelogram as well!