My presentation is about polygons. Polygons are everywhere. They are in art, on buildings, signs, and many other things around our homes.
The word polygon means many angles. Polygons are 2-dimensional closed shapes. They are made up of 3 or more straight lines segments. These line segments are all connected so that it is closed.
Polygons do not have line segments that cross. They also cannot be curved nor not connected to another line segment. Non-examples of polygons are circles, stars that have lines that cross, and half moons.
Polygons can be convex or concave. A convex polygon has all interior angles less than 180 degrees. A concave polygon has one or more interior angles greater than 180°.
There are parts of polygons which help define properties of polygons. There are sides, vertices: where two sides meet, diagonals: line connecting two nonadjacent vertices, interior angles: angles inside the closed figure, exterior angles: angles on the outside of the polygon.
The number of sides defines the names of the polygons. 3 sides is a triangle, 4 sides is quadrilateral, 5 sides is a pentagon and so on.
Polygons can be equiangular and equilateral. Equiangular polygon are polygons where all angles are equal. Equilateral polygons has sides that are all equal. Polygons that are both equilateral and equiangular a called regular polygons.
We talked about the different triangles and their properties in chapter 4. We learn the isosceles, scalene, and right triangles. We also learned about the measurements of the angles and sides of these triangles and how they relate. We learn about theorems like AAS, SAS, and more which we can use to prove things about triangles.
As we did with triangles in chapter 4, in this chapter we will learn about the properties of quadrilaterals and how we can use them to classify them.
A quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals. The five most common types are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus.
Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on.
We see quadrilaterals everywhere. T.V.s, pictures frames, kites, houses, and art. These are the most common polygons we see in our everyday life.
In this chapter we will learn different vocabulary like the different names of quadrilaterals and midsegment of a trapezoid. We will use this various vocabulary to talk about the quadrilaterals and prove various theorems about quadrilaterals.
The sum of the interior angles of a quadrilateral is 360 degrees. We find this using the formula (n-2)180 degree. Since n=4 we have 360 degrees as our sum.
There are unique properties dealing with the angles measures, side lengths, and parallel lines. We can use the properties of each quadrilateral to classify them into each type.
Using the properties all "quadrilaterals" can be separated into three sub-groups: general quadrilaterals, parallelograms and trapezoids.
A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. A rhombus is defined as a parallelogram with four equal sides. Is a rhombus always a rectangle? No, because a rhombus does not have to have 4 right angles. Trapezoids only have one pair of parallel sides. It's a type of quadrilateral that is not a parallelogram. Kites have two pairs of adjacent sides that are equal.
Using the properties we can find prove figures are quadrilaterals and more specifically what kind of quadrilateral. We can also find angle measures and side lengths when given various information.
Quadrilaterals are some of the most common polygons we see and we will use the information we learn about in this chapter in the future when we talk about transformations and 3-dimensional objects.