📐 Advanced Geometry Study Guide
🔺 1. Foundations of Geometry
Key Concepts
● Points, lines, planes
● Segments, rays, angles
● Angle types: acute, right, obtuse, straight
● Vertical angles = congruent
● Linear pairs = supplementary (sum = 180°)
Must-Know Rules
● Complementary: add to 90°
● Supplementary: add to 180°
● Around a point: 360°
📏 2. Triangle Geometry
Triangle Types
● Scalene: no equal sides
● Isosceles: two equal sides
● Equilateral: all equal (each angle = 60°)
Core Theorem
● Triangle Angle Sum: a + b + c = 180°
Special Theorems
● Exterior angle = sum of remote interior angles
● Isosceles base angles are equal
● Triangle Inequality: sum of any two sides > third side
📐 3. Right Triangles & Trigonometry
Pythagorean Theorem: a² + b² = c²
Trig Ratios (SOH-CAH-TOA)
● sin = opposite / hypotenuse
● cos = adjacent / hypotenuse
● tan = opposite / adjacent
Special Triangles
● 45-45-90 → sides: x,x,x and 2 squared
● 30-60-90 → sides: x,x 3 squared, 2x
🔺 1. Foundations of Geometry
Key Concepts
● Points, lines, planes
● Segments, rays, angles
● Angle types: acute, right, obtuse, straight
● Vertical angles = congruent
● Linear pairs = supplementary (sum = 180°)
Must-Know Rules
● Complementary: add to 90°
● Supplementary: add to 180°
● Around a point: 360°
📏 2. Triangle Geometry
Triangle Types
● Scalene: no equal sides
● Isosceles: two equal sides
● Equilateral: all equal (each angle = 60°)
Core Theorem
● Triangle Angle Sum: a + b + c = 180°
Special Theorems
● Exterior angle = sum of remote interior angles
● Isosceles base angles are equal
● Triangle Inequality: sum of any two sides > third side
📐 3. Right Triangles & Trigonometry
Pythagorean Theorem: a² + b² = c²
Trig Ratios (SOH-CAH-TOA)
● sin = opposite / hypotenuse
● cos = adjacent / hypotenuse
● tan = opposite / adjacent
Special Triangles
● 45-45-90 → sides: x,x,x and 2 squared
● 30-60-90 → sides: x,x 3 squared, 2x
