2-D Angles & Triangles

What does it mean?

Angle Definitions:

Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

Converse also true:
If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.

https://www.mathsisfun.com/geometry/alternate-exterior-angles.html

Triangle Definitions:

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent.

If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally

If MBP is any triangle and LA is drawn parallel to MB, then PL/CE = PA/CE

What does it look like?

A general example to help you recognize patterns and spot the information you're looking for

Angles

Alternate Angles:
∠A = ∠H ∠G = ∠B

The angles inside a letter "Z" are alternate interior angles...

Triangles

△ ADE and △ ABC are similar as they are equiangular. $$\frac{AD}{AB} = \frac{DE}{BC}$$ $$\frac{x + 4}{x} = \frac{6}{3}$$ $$\frac{x + 4}{x} = 2$$ $$x(\frac{x + 4}{x}) = x * 2$$ $$x + 4 = 2x$$ $$x + 4 - x = 2x - x$$ $$4 = x$$ $$x = 4$$