Circle Geometry and Triangle Types
This page provides a comprehensive overview of various geometric concepts, focusing on circle geometry and different types of triangles. It serves as a quick reference guide for students studying mathematics, particularly geometry and trigonometry.
The page begins by illustrating the key components of a circle, including the diameter, radius, and chord. It then introduces the concept of the perpendicular bisector of a chord of a circle, which is a fundamental principle in circle geometry.
Definition: A chord bisector is a line that divides a chord of a circle into two equal parts and is perpendicular to the chord.
The document also covers different types of triangles, with a focus on isosceles triangles.
Vocabulary: An isosceles triangle is a triangle with two sides of equal length and two equal angles opposite those sides.
Various geometric theorems are presented, including:
- The sum of angles in a triangle equals 180°
- The sum of angles around a point equals 360°
- Angles on a straight line sum to 180°
The page also introduces trigonometric ratios (SOH CAH TOA) and the sine and cosine rules, which are essential for solving problems involving triangles.
Example: The sine rule states that for any triangle ABC, a/sin A = b/sin B = c/sin C, where a, b, and c are the lengths of the sides opposite to angles A, B, and C respectively.
Other mathematical concepts covered include:
- Probability formulas
- Statistical measures (median, quartiles, interquartile range)
- Area formulas for various shapes
- Density calculations
- Quadratic formula
- Cumulative frequency graphs and pie charts
Highlight: The page provides a comprehensive collection of formulas and theorems, making it an excellent quick reference for students studying geometry and related mathematical topics.
The document concludes with additional formulas and concepts, including:
- Polygon angle properties
- Surds
- Pythagoras theorem
- Volume calculations
- Data analysis (mode, median, mean, range)
- Percentage calculations
- Interest calculations (simple and compound)
- Sequences and series
- Equation of a straight line
This page serves as a valuable resource for students, providing a wide range of mathematical concepts and formulas in a concise, easy-to-reference format.
