Geometry Basics Quiz

Point: A location in space with no dimensions.
Line: A straight path extending infinitely in both directions with no thickness.
Line Segment: A part of a line with two endpoints.
Ray: A part of a line that starts at a point and extends infinitely in one direction.
Plane: A flat, two-dimensional surface that extends infinitely in all directions.

Angle: Formed by two rays with a common endpoint (vertex).
Types of Angles:
- Acute: Less than 90 degrees.
- Right: Exactly 90 degrees.
- Obtuse: More than 90 degrees but less than 180 degrees.
- Straight: Exactly 180 degrees.
Complementary Angles: Two angles that sum to 90 degrees.
Supplementary Angles: Two angles that sum to 180 degrees.

Types of Triangles:
- By Sides:
  - Equilateral: All sides equal.
  - Isosceles: Two sides equal.
  - Scalene: No sides equal.
- By Angles:
  - Acute: All angles less than 90 degrees.
  - Right: One angle equals 90 degrees.
  - Obtuse: One angle greater than 90 degrees.
Properties:
- The sum of interior angles in a triangle is always 180 degrees.

Types of Quadrilaterals:
- Square: All sides equal and angles 90 degrees.
- Rectangle: Opposite sides equal and angles 90 degrees.
- Rhombus: All sides equal but angles not necessarily 90 degrees.
- Trapezoid: At least one pair of parallel sides.
Properties:
- The sum of the interior angles in a quadrilateral is always 360 degrees.

Definitions:
- Center: The point equidistant from all points on the circle.
- Radius: Distance from the center to any point on the circle.
- Diameter: Twice the radius, a line segment through the center with endpoints on the circle.
- Circumference: Distance around the circle, calculated as C = πd or C = 2πr.
- Area: Space enclosed by the circle, calculated as A = πr².

Coordinate Plane: Consists of two perpendicular axes, x (horizontal) and y (vertical).
Points: Represents as (x, y) where x is the horizontal position and y is the vertical position.
Distance Formula: The distance between two points (x1, y1) and (x2, y2) is given by:
- ( d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} )
Midpoint Formula: The midpoint M between two points (x1, y1) and (x2, y2) is given by:
- ( M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right) )

3D Shapes:
- Cube: A three-dimensional figure with 6 equal square faces.
- Rectangular Prism: A three-dimensional figure with 6 rectangular faces.
- Cylinder: Has two parallel circular bases connected by a curved surface.
- Sphere: A perfectly round three-dimensional object with all points on the surface equidistant from the center.
Volume and Surface Area:
- Cube: Volume = ( s^3 ), Surface Area = ( 6s^2 )
- Cylinder: Volume = ( πr^2h ), Surface Area = ( 2πrh + 2πr^2 )
- Sphere: Volume = ( \frac{4}{3}πr^3 ), Surface Area = ( 4πr^2 )

Pythagorean Theorem: In a right triangle, ( a^2 + b^2 = c^2 ) where c is the hypotenuse.
Triangle Similarity: If two triangles have the same angle measures, they are similar regardless of the lengths of their sides.
Congruence: Two figures are congruent if they have the same shape and size.

Point: A fixed position in space with no size or dimensions.
Line: A straight path extending infinitely in both directions, with no thickness.
Line Segment: A portion of a line defined by two endpoints.
Ray: A part of a line that starts at a specific point and extends infinitely in one direction.
Plane: A flat surface that extends infinitely in all directions.

Angle: Formed by two rays sharing a common endpoint, known as the vertex.
Angle Types:
- Acute Angle: Measures less than 90 degrees.
- Right Angle: Measures exactly 90 degrees.
- Obtuse Angle: Measures more than 90 degrees but less than 180 degrees.
- Straight Angle: Measures exactly 180 degrees.
- Complementary Angles: Two angles that add up to 90 degrees.
- Supplementary Angles: Two angles that add up to 180 degrees.

Triangle Types:
- Based on Sides:
  - Equilateral: All sides are equal.
  - Isosceles: Two sides are equal.
  - Scalene: All sides are different.
- Based on Angles:
  - Acute Triangle: All angles are less than 90 degrees.
  - Right Triangle: One angle measures 90 degrees.
  - Obtuse Triangle: One angle measures greater than 90 degrees.
Key Property: The sum of interior angles in any triangle always equals 180 degrees.

Quadrilateral Types:
- Square: All sides are equal, and all angles are right angles (90 degrees).
- Rectangle: Opposite sides are equal, and all angles are right angles.
- Rhombus: All sides are equal, but angles may not be right angles.
- Trapezoid: At least one pair of opposite sides are parallel.
Important Fact: The sum of interior angles in a quadrilateral always amounts to 360 degrees.

Key Definitions:
- Center: The point equidistant from all points on the circle.
- Radius: Distance from the center to any point on the circle.
- Diameter: Twice the radius, a straight line segment passing through the center and having endpoints on the circle.
- Circumference: The distance around the circle, calculated using the formula C = πd or C = 2πr, where d is the diameter and r is the radius.
- Area: The space enclosed by the circle, calculated using the formula A = πr², where r is the radius.

Coordinate Plane: A plane formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical).
Point Representation: A point is represented by an ordered pair (x, y) where x is the horizontal coordinate and y is the vertical coordinate.
Distance Formula: Used to calculate the distance between two points (x1, y1) and (x2, y2):
- ( d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} )
Midpoint Formula: Used to find the midpoint M between two points (x1, y1) and (x2, y2):
- ( M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right) )

3D Shapes:
- Cube: A three-dimensional figure with six equal square faces.
- Rectangular Prism: A three-dimensional figure with six rectangular faces.
- Cylinder: Has two parallel circular bases connected by a curved surface.
- Sphere: A perfectly round, three-dimensional object with all points on its surface equidistant from the center.
Important Formulas:
- Cube:
  - Volume = ( s^3 ) (where s is the side length)
  - Surface Area = ( 6s^2 )
- Cylinder:
  - Volume = ( πr^2h ) (where r is the radius and h is the height)
  - Surface Area = ( 2πrh + 2πr^2 )
- Sphere:
  - Volume = ( \frac{4}{3}πr^3 ) (where r is the radius)
  - Surface Area = ( 4πr^2 )

Pythagorean Theorem: In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: ( a^2 + b^2 = c^2 ).
Triangle Similarity: Two triangles are similar if their corresponding angles are equal.
Congruence: Two geometric figures are congruent if they have the same shape and size.