Geometry: Equations of Lines and Angles in Polygons

Equations of Lines

• A line's equation is typically written as where represents the gradient (slope) and shows the y-intercept.
• To find an equation between two points, first calculate the gradient using the formula .
• Then, substitute the coordinates of one point into the equation to determine .
• Parallel lines share the same gradient.
• Perpendicular lines have gradients that are negative reciprocals of each other. If a line has a gradient of , a perpendicular line will have a gradient of .

Angles in Polygons

• The sum of interior angles in a polygon with sides is given by the formula .
• The sum of exterior angles in any polygon is always 360°.
• The measure of each exterior angle in a regular polygon with sides is found using the formula.
• The measure of each interior angle in a regular polygon is calculated.

Algebra in Angles of Polygons

• Algebraic equations can be set up and solved to find unknown angles within polygons.
• Basic algebraic principles are applied to solve for unknown values.

Speed, Density & Pressure

• Speed is calculated by dividing distance by time (e.g., meters/second).
• Density is determined by mass divided by volume.
• Pressure describes the force per unit area acting on a surface.

Pythagoras’ Theorem (2D)

•  Pythagoras' Theorem is used to find the lengths of sides within right-angled triangles.
• The core formula is . (where c represents the hypotenuse and a and b represent the other two sides.)
• When dealing with word problems, identify the right triangles involved, and then systematically apply the theorem to find the required lengths.

Trigonometry

• Use SOH CAH TOA to relate trigonometric ratios (sine, cosine, tangent) to sides of right-angled triangles: to find lengths or angles.
• Rearrange the trigonometric formulas as needed to find sides. e.g., if you know the angle and the adjacent side to find the hypotenuse, solve , use inverse functions to find missing angles. .
• Finding angles: inverse trigonometric functions (arcsin, arccos, arctan) are used to find the angles
• Example: If , then represents an angle whose tangent is 0.75.

Revision Strategies

• Solving past paper questions helps reinforce understanding.
• Using flashcards for formulas serves as a constant review.
• Explaining concepts to a friend helps solidify your comprehension.
• Practice problems step-by step improves accuracy in calculations .