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 .

This quiz covers key concepts in geometry, focusing on the equations of lines including gradients and y-intercepts, as well as the properties of angles in polygons. Students will learn to calculate interior and exterior angles and solve related algebraic equations. Test your knowledge to master these essential geometric principles!