Geometry Basics
What is the perimeter of a regular polygon?
Adjacent angles are two angles that share a common vertex and a common side but do not overlap. They lie next to each other.
Identify the angle and which sides are involved (opposite, adjacent, hypotenuse), choose the appropriate ratio (sin, cos, or tan), set up the equation, and solve for the unknown side. For example, if you know angle θ and the hypotenuse, use opposite = hypotenuse × sin θ.
A dilation is a transformation that enlarges or reduces a figure by a scale factor k from a center point. It maps (x, y) to (kx, ky) when centered at the origin.
The perimeter of a regular polygon is P = n × s, where n is the number of sides and s
Geometry Basics
What is a rotation in geometry?
A rotation turns a figure around a fixed point called the center of rotation by a specified angle. It preserves size, shape, and the distance of each point from the center.
Using a² + b² = c²: 3² + 4² = 9 + 16 = 25, so c = √25 = 5. This is the most well-known Pythagorean triple: (3, 4, 5).
The distance between two points (x₁, y₁) and (x₂, y₂) is d = √[(x₂−x₁)² + (y₂−y₁)²]. It is derived from the Pythagorean Theorem.
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).
Geometry Basics
What is a tangent line to a circle?
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).
A tangent is a line that touches the circle at exactly one point, called the point of tangency. A tangent is always perpendicular to the radius drawn to the point of tangency.
The sine of an angle θ is the ratio of the length of the side opposite the angle to the hypotenuse: sin θ = opposite / hypotenuse.
First calculate the slope m = (y₂−y₁)/(x₂−x₁), then substitute m y − y₁ = m(x − x₁). Simplify to your preferred form.
Geometry Basics
What are vertical angles?
Alternate interior angles are on opposite sides of the transversal and between the parallel lines. When the lines are parallel, they are congruent.
Identify the angle and which sides are involved (opposite, adjacent, hypotenuse), choose the appropriate ratio (sin, cos, or tan), set up the equation, and solve for the unknown side. For example, if you know angle θ and the hypotenuse, use opposite = hypotenuse × sin θ.
Vertical angles are the pairs of opposite angles formed when two lines intersect. They are always congruent (equal in measure).
Equilateral (all three sides equal), isosceles (exactly two sides equal), and scalene (no sides equal). Each type also has corresponding angle properties.