(undecided if I should apologise for subjecting you to math at 10.30pm 🙈🙈🙈, but will probs keep doing it 🤣)
Moar geometry basics 🥰🦕🤩😄
Got to the special angles section of vocab and my brain was like nope.
So combination of chatgpt breaking it down, and lots of visuals via google and YouTube and sketching them out myself finally helped me understand what corresponding angles are (plus the other stuff).
In jargon speak they are angles in the same relative position created when lines are crossed by a transversal (this is the nope part 😭😵).
In a way my brain can understand:
Imagine train tracks without the rungs, with a long rung laid on top of the tracks so it cuts through both of them. The rung is the transversal (trespasses, transverses).
At the point the rung cuts across the tracks (intersection point), four angles are created. The same happens at the other intersection on the opposite side.
The angle on the top right, corresponds to the same angle at the top right of the opposite intersection point.
The picture I drew with the blue, green, yellow and red angles helped it click for me. The same colour angles are corresponding.
Looking forward to discovering the practical use cases for these when getting to the construction part of this geometry book.
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I'm writing the rest out the next day, to see how much I can remember without reading the page attached at the top.
Special Lines
Transversal: A line that crosses over two or more other lines. This was not part of the special lines section, but the special angles section. But still the first one that came to mind.
Segment Bisector: A line that crosses through the midpoint of a line segment.
Angle Bisector: A line that starts at the vertex of an angle and divides it into two congruent parts.
Parallel: Two lines that are opposite each other on the same plane, going in the same direction, and equal distances apart across the whole line. If there's a slight tilt to one of them then eventually they will intersect, which means they are not parallel.
Perpendicular: Two lines that are at a 90 degree angle to each other.
Special Angles
Special angles are named based on their position to one another.
Adjacent: Two angles that share a vertex and a single side, that do not overlap.
Corresponding: When a transversal cuts across one or more lines, each intersection point creates four angles, like the face of a clock with four segments. The top right segment in the upper intersection corresponds to the angle at the top right segment in the lower intersection (or left or right). This is very hard to explain without a drawing. The angles that are relative to one another (more jargon that means nothing to me even if it's correct).
Vertex: The point of an angle where the end of two rays, two segments or 1 ray and 1 segment meet.
Congruent: Where a shape has the exact same dimensions and can be placed one on top of the other as a perfect match.
Alternate interior: Back to the corresponding angle example, the inner angles inside both of the lines intersected by the transversal, on opposite sides. Will be congruent if the lines traversed are parallel.
Alternate exterior: The outer angles outside of the lines intersected by the transversal, on opposite sides. Will be congruent if the lines traversed are parallel.
Supplemental: Made up of two angles whose degrees add up to 180.
What's missing?
Special lines
After reading the page, I got all of the special lines apart from "Angle", which is okay because why is that even in that section.
Special angles
Vertical: Two angles that are opposite each other and share a vertex but no sides, that look like an X. X marks the spot.
Same-side interior: Same as alternate interior except on the same side not alternating. Looks like a C shape.
Same-side exterior: Same as alternate exterior except on the same side not alternating.
Pretty happy with that result. Not going to try remembering these again, I know where to find the definitions now, and they should sink in more when I get past the vocab into practical constructions.
