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# Geometry Basics

Created by
@BetterYeti

### What is a point in space?

A set of coordinates (x, y, z) with no size, only position

### What is a line defined by?

Two points or a point and a slope

### What is an angle?

A figure formed by two rays sharing a common endpoint (vertex)

### What is a triangle?

<p>A polygon with three sides and three angles</p> Signup and view all the answers

<p>A polygon with four sides and four angles</p> Signup and view all the answers

### What is a circle?

<p>A set of points equidistant from a central point (center)</p> Signup and view all the answers

### What is the center of a circle?

<p>The fixed point equidistant from all points on the circle</p> Signup and view all the answers

### What is the radius of a circle?

<p>The distance from the center to any point on the circle</p> Signup and view all the answers

### What type of angle is greater than 180 degrees but less than 360 degrees?

<p>Reflex angle</p> Signup and view all the answers

### What type of triangle has one right angle (90 degrees)?

<p>Right triangle</p> Signup and view all the answers

## Study Notes

### Points

• A point is a location in space, represented by a set of coordinates (x, y, z)
• It has no size, only position

### Lines

• A line is a set of points extending infinitely in two directions
• It can be defined by two points or a point and a slope
• Line properties:
• Collinear points: points that lie on the same line
• Intersecting lines: lines that share a common point
• Parallel lines: lines that never intersect, always the same distance apart
• Perpendicular lines: lines that intersect at a 90-degree angle

### Angles

• An angle is formed by two rays sharing a common endpoint (vertex)
• Angle properties:
• Acute angle: less than 90 degrees
• Right angle: exactly 90 degrees
• Obtuse angle: greater than 90 degrees but less than 180 degrees
• Straight angle: exactly 180 degrees
• Reflex angle: greater than 180 degrees but less than 360 degrees

### Triangles

• A triangle is a polygon with three sides and three angles
• Triangle properties:
• Equilateral triangle: all sides are equal
• Isosceles triangle: two sides are equal
• Scalene triangle: all sides are unequal
• Right triangle: one right angle (90 degrees)
• Oblique triangle: no right angles

• A quadrilateral is a polygon with four sides and four angles
• Rectangle: all angles are right angles, opposite sides are equal
• Square: all sides are equal, all angles are right angles
• Rhombus: all sides are equal, opposite sides are parallel
• Trapezoid: two pairs of opposite sides, at least two sides are parallel

### Circles

• A circle is a set of points equidistant from a central point (center)
• Circle properties:
• Center: the fixed point equidistant from all points on the circle
• Radius: the distance from the center to any point on the circle
• Circumference: the distance around the circle
• Diameter: the longest distance across the circle, passing through the center

### Points

• A point is a location in space, represented by a set of coordinates (x, y, z) with no size, only position.

### Lines

• A line is a set of points extending infinitely in two directions, definable by two points or a point and a slope.
• Collinear points lie on the same line.
• Intersecting lines share a common point.
• Parallel lines never intersect and are always the same distance apart.
• Perpendicular lines intersect at a 90-degree angle.

### Angles

• An angle is formed by two rays sharing a common endpoint (vertex).
• Acute angles are less than 90 degrees.
• Right angles are exactly 90 degrees.
• Obtuse angles are greater than 90 degrees but less than 180 degrees.
• Straight angles are exactly 180 degrees.
• Reflex angles are greater than 180 degrees but less than 360 degrees.

### Triangles

• A triangle is a polygon with three sides and three angles.
• Equilateral triangles have all sides equal.
• Isosceles triangles have two sides equal.
• Scalene triangles have all sides unequal.
• Right triangles have one right angle (90 degrees).
• Oblique triangles have no right angles.

• A quadrilateral is a polygon with four sides and four angles.
• Rectangles have all angles as right angles, with opposite sides equal.
• Squares have all sides equal, with all angles as right angles.
• Rhombi have all sides equal, with opposite sides parallel.
• Trapezoids have two pairs of opposite sides, with at least two sides parallel.

### Circles

• A circle is a set of points equidistant from a central point (center).
• The center is the fixed point equidistant from all points on the circle.
• Radius is the distance from the center to any point on the circle.
• Circumference is the distance around the circle.
• Diameter is the longest distance across the circle, passing through the center.

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## Description

Understand the fundamental concepts of geometry, including points, lines, and their properties. Learn about collinear points, intersecting lines, parallel lines, and perpendicular lines.

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