Poly-WHUT?

This is a video I really wanted to post because it explains the difference between a polygon and a polyhedron in less than 2 minutes. I hope you find it super helpful!

Polygon - 2D

Polyhedron - 3D

3D Geometry

Looking at 3D geometry is interesting. Well, at least I think so since I can't draw for the life of me. In this post I'll break down geometry that comes in three dimensions.

Simple closed surface: has exactly one interior, no holes, and is hollow. An example of this would be a sphere. 

Polyhedron: a simple, closed surface made up of polygonal faces. An example of this would be a soccer ball. 

See how the ball is made up of a whole bunch of hexagons and pentagons?

Prism: a polyhedron in which two congruent faces (bases) lie in parallel planes and the other faces (lateral faces) are bounded by parallelograms. The name of the prism starts with the name of the bases.

For example:

Hexagonal Prism

Octagonal Prism

Triangular Prism

Not too bad so far, right? Stick with me!

Pyramids: Polyhedron determined by a polygon and a point not in the plane of the polygon. Just like the prism, the name of the pyramid is determined by the shape of the base. 

Regular polyhedra: a convex polyhedron whose faces are identical regular polygons.

Examples:

Cylinder: a simple, closed surface that is NOT a polyhedron. Has two simple closed curves called bases and a lateral surface.

Cone: the union of line segments connecting to a point.

Quirky Quads

The topic of quadrilaterals is pretty big, so it gets its own post. A quadrilateral is simply a four-sided polygon. Four sides. Four angles. And yes.... we're still talking about polygons! :)

It's important to note that the measure of the interior angles of a quadrilateral is 360°.

For example, this quadrilateral is a rectangle:

Each angle (a,b,c,d) is 90°.

90°+90°+90°+90°=360°

Does that make sense so far?

Unlike other polygons, quadrilaterals are put into a hierarchy. Here's a map to explain what I mean:

Although they are all 4-sided quadrilaterals, they are put into categories based on different properties. The kite has no pairs of parallel sides. The trapezoid has one pair of parallel sides. The parallelogram, rectangle, rhombus, and square all have two pairs of parallel sides. You should note that the rectangle and square are made up of right angles.

Once again, a video! 

Seriously, I highly recommend this guy!

 

Tricky Triangles

You're in luck... there are only three types of triangles! Yay!

Let's get down to business... and then I'll attach another awesome video at the end for your enjoyment :)

Scalene: no congruent sides (all sides are different)

Isosceles: at least two congruent sides

Equilateral: all three sides are congruent

Okay, maybe I lied... there are three more kinds of triangles! Oops! But it connects to the post about the types of angles so it's pretty easy.

ONE MORE THING: 

The sum of the measure of the interior angles of a triangle always equals 180°

For example:

This is an equilateral triangle, so each angle measures 60°.

60°+60°+60°=180°

This is a scalene triangle. Each angle measures differently.

60°+50°+70°=180°

TRY IT!

40°+70°=110°

180°-110°=70°

Therefore, this is an isosceles triangle.

And now the moment you've been waiting for... ;)

Okay, maybe it's not too exciting... but it helps, right?!

I honestly do recommend subscribing to Math Antics on YouTube :) He has many more math topics he covers!

Pretty, Pretty Polygons

A polygon is a simple, closed curve with sides that are line segments. 
A regular polygon means that all sides and angles are congruent - exactly the same!

This is a simple and helpful table to help you sort out the different kinds of polygons!

This is an amazing video that really breaks down polygons!

What's your angle?

Angle: formed by two rays with the same endpoint

Vertex: the common endpoint of the two rays that form an angle (customary to name an angle by its vertex)

Types of Angles:

Straight: exactly 180°

Acute: less than 90°

Obtuse: more than 90°, less than 180°

Right: exactly 90°

Adjacent: share a common side and vertex, but do not overlap interiors

Vertical: created by intersecting lines which are pairs of angles whose sides are two pairs of opposite rays. They are congruent (exactly the same)!

Supplementary: two angles whose sum of measure is 180°

Since you are given 60°, you can solve

 angle WYZ by 180°-60°=120°

Complementary: two angles whose sum of measure is 90°

30°+60°=90°

Transversal: angles formed by a transversal line

 Line t is intersecting two coplanar lines l1 and l2. 

The line t is called the transversal.

Super helpful videos!

Angle Basics

Angles & Degrees

Back to Basics

The basic building blocks of geometry are points, lines, and planes.

A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. 

These are points C, M, Q

Types of Lines:
Line: has no thickness and extends forever in two directions

Collinear points: points on the same line

Line segment: a connected piece of a line. It has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment. 

This is line segment CD

Ray: a piece of a line, except that it has only one endpoint and continues forever in one direction

Intersecting lines: lines with exactly one point in common

Skew lines: two nonparallel lines in space that do not intersect

ST and UV are skew lines

Concurrent lines: three of more lines that intersect in the same point

lines l, m, n are intersect point p

Parallel lines: coplanar lines that have no points in common

Perpendicular lines: two lines that intersect and form right angles

A plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, infinite width, and zero height (or thickness). It is usually represented in drawings by a four‐sided figure. A single capital letter is used to denote a plane. 

More fantastic and easy-to-understand information can be found at Cliff Notes, I Coach Math, and Math Captain.