## Angles and Vectors

### Angles and Lines

**Complementary angles** add up to 90'

**Supplementary angles** add up to 180'

**alternative angles** are equal (congruent angles on transversal line intersecting two parallel lines)

**vertical angles theorem** says that angles opposite one another when two straight lines intersect are congruent

In the diagram shown, <b₁ and <c are complementary, as are <e and <f. Angles <b₁ and <d are supplementary. Because of alternative angles of parallel lines, <b₂ = <b', and <d = <d' (assuming lines Y and Z are parallel). From the vertical angles theorem, <b₁ = <b₂.

Distance between two points = √(Δx² + Δy²) (based on Pythagorean theorem)

### Vectors (Rays)

Length of a vector can be written as ||v|| (the "norm" of vector v)

Distance of two vectors: first add the vectors to make a combined vector. To add vectors, simply add each part of the vector, ie. (x1 + x2, y1 + y2)

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