Geometry - Polygons, Parallel lines, Quadrilaterals, Triangles, and Transformation

What transformations are rigid motions?

Translations, Rotations, and Reflections

What motion is not a rigid motion?

Dilation

If two lines are parallel what relationship does a line intersecting both have with its angles?

1 + 5, 4 + 8, 6 + 2, 3 + 7, are corresponding angles meaning they’re congruent. 3 + 5, 2 + 8 are supplementary meaning they add up to 180 degrees they are know as consecutive interior angles. 3+4, 1+2, 5+6, 7+8 are all vertical angles meaning they are congruent. 3 + 8, 2 + 5 are congruent because they are alternate interior angles. 7 + 4, 1 + 6 are congruent because they are alternate exterior angles.

What are the traits of an isosceles trapezoid?

They have congruent legs (AB, DC) along with congruent base angles (angle B, angle C) and their diagonals (AC, DB) are congruent.

What are the traits of a parallelogram?

They have parallel opposite sides and opposite sides are congruent. Opposite angles are congruent, consecutive angles are supplementary (180), and its diagonals bisect (split into two equal parts) eachother.

What are the trait of a rectangle?

A rectangle is a parallelogram with 4 right angles and congruent diagonals

What are the traits of a rhombus?

A parallelogram with 4 congruent sides, and with diagonals that bisect each other perpendicularly (creates a 90 degree angle)

Whats are the traits of a square?

Both the traits of a rectangle and a rhombus combined.

Whats a scalene triangle?

A triangle with no congruent sides.

Whats an isosceles triangle?

A triangle with two congruent legs (left and right sides)

What’s an equilateral triangle?

A triangle with 3 congruent sides.

Whats an acute triangle?

A triangle with all acute interior angles (<90)

What’s an obtuse triangle?

A triangle with one obtuse angle (>90)

What’s an right triangle?

A triangle with one right angle (==90)

Whats an Equiangular triangle?

A triangle with all congruent angles (60), is also an equilateral triangle no matter what

What degrees does the interior angles of a triangle add up to?

180 degrees

What is the theory behind the exterior angle of a triangle?

The two non-adjacent angles add up to the exterior angle.

What’s the Pythagorean therom?

a² + b² = c²

How do you find the area of a triangle?

$$\frac12bh$$

How do you find the area of a triangle using trig?

$$\frac12ab\sin\left(C\right)$$

What is the relationships between triangle sides and trig functions?

sin = S, C = cos, T = tan, O = opposite, H = hypotenuse, A = adjacent S = O/H, C = A/H, T = O/A

Whats the relationship in trig functions between the two non-right angles in a right triangle

Sin(A) = Cos(B)