Today I'm going to get into Geometry a little bit more today. I've been reading up and learning more about the basic knowledge of Geometry. I'll be telling you guys about vertical angles. For me, Geometry has always been super hard. I've always struggled with it, but learning step by step and having a deeper understanding has helped me a ton these past few weeks.
First off, there are three types of angles: vertical, supplementary, and complementary angles. Vertical angles are created by intersecting a pair of angles whore sides are two pairs of opposite rays. Vertical angles look like this:
Angles 1 and 3 would be vertical angles and angles 2 and 4 would be the other vertical angles. All vertical angles are congruent.
Supplementary angles are angles that have a measurable sum of 180 degrees. Here is an example of a supplementary angle:
Supplementary angles will always have a formula to figure out the angles of it. Here's what it looks like:
So the formula would be (180 - 65) = x
Complementary angles are the same as supplementary angles, but the angles add up to 90 degrees instead of 180 degrees. Here's an example:
To figure out the complementary angles, you use this formula:
It's similar to the supplementary angle formula, but you just put in 90 degrees instead of 180 degrees.
Now since we have an understanding of vertical, supplementary, and complementary angles, we can get into a deeper understanding of angles. Transversal lines are two parallel lines intersected by a third line at an angle. The third line would be the transversal. On the parallel and transversal lines, there are different angles. In between each line is considered an angle. Here's an example:
The different angles inside and outside of the transversal and parallel lines have specific names. The interior angles are the angles on the inside. The interior angles in the picture would be numbers 3, 4, 5, and 6. The exterior angles would be on the outside. The exterior angles would be 1, 2, 7, and 8. Since we have those in mind, we can talk about alternate interior and exterior angles.
Alternate interior and exterior angles would be the angles that are opposite of each other. An example of an alternate interior angle would be angles 3 and 6. They are on the inside of the parallel and transversal lines but they are on opposite ends. An example of an alternate exterior angle would be angles 2 and 7.
There's also another type of transversals and angles. It is called corresponding angles. They are a little bit easier to understand. Corresponding angles are the angles that occupy the same relative position at each intersection where a straight line crosses two others (aka the transversal line). The corresponding angles on the picture would be angles 2 and 6, 4 and 8, 1 and 5, 3 and 7.
There's a property in Geometry that goes with angles and parallel lines. It is: If any two distinct coplanar lines are cut by a transversal, then a pair of corresponding angles, alternate interior angles, or alternate exterior angles are congruent if, and only if, the lines are parallel.
So that's all tonight about exploring a little bit into Geometry. In my next post, I'll talk a little bit more about Geometry. I hope you guys have a great night and here's a video talking about what I just did today!
