Area of a Triangle
? Video Tutorial Area of a Triangle: The area of a triangle is half of the base multiplied by the height. Choosing the Base and Height: To calculate the area, choose any side of the triangle as the base, and the height is the perpendicular distance from this base to the opposite vertex. Example on […]
Area of Compound Shapes
? Video Tutorial Definition of Compound Shape: A compound shape is formed by combining simple shapes (e.g., rectangles, triangles, circles). Method and Examples for Finding Area: Break down the compound shape, calculate each simple shape’s area, and then add or subtract as necessary based on the layout of the compound shape. Application – Painting Cost Calculation: […]
Rotational Symmetry
? Video Tutorial Rotational Symmetry: A shape has rotational symmetry if it can be rotated less than 360° and still look the same. Centre of Rotation: The fixed point around which a shape rotates. For most regular polygons, it’s the geometric center. Order of Symmetry: The number of times a shape matches itself during a […]
Line of Symmetry
? Video Tutorial Definition of Line of Symmetry: A line of symmetry divides a shape into two identical, mirror-image halves. Reflection Symmetry: Shapes like rectangles, squares, and circles have reflection symmetry because they have at least one line of symmetry. Mirror Points: Every point on one side of the line of symmetry has a corresponding […]
Pythagoras’ Theorem and Applications
? Video Tutorial Pythagoras’ Theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides $(a^2 + b^2 = c^2)$. Finding the Missing Side of a Triangle: Substitute known side lengths into the equation to solve for the unknown side. Coordinate Geometry Application: Determine the […]
Trigonometry: Sine, Cosine, Tangent
? Video Tutorial Basic Trigonometry: Sine, cosine, and tangent depend only on the angle $theta$ in a right-angled triangle; they do not change with the size of the triangle. Trigonometric Ratios: $sin theta = large frac{text{opposite}}{text{hypotenuse}}$, $cos theta = large frac{text{adjacent}}{text{hypotenuse}}$, $tan theta = large frac{text{opposite}}{text{adjacent}}$. Solving for Sides: Use trigonometric ratios with a known […]
Cosine Rule
? Video Tutorial Cosine Rule: Use it to find missing sides or angles in non-right-angled triangles. Cosine Rule Formula: For any triangle, the formula is: $a^2 = b^2 + c^2 – 2bc cdot cos(A)$, where $A$ is the angle opposite side $a$. Finding a Missing Side: If two sides and the included angle are known, […]
Sine Rule
? Video Tutorial Sine Rule Formula: The ratio of each side length to the sine of its opposite angle is consistent throughout the triangle. The formula is: $large frac{a}{sin A} = frac{b}{sin B} = frac{c}{sin C}$. Sine Rule Application: Helps to calculate missing sides or angles in any triangle, as long as one angle-side pair […]
Circumference and Area of a Circle and a Sector
? Video Tutorial Circumference of a Circle: $C = pi d$ or $C = 2pi r$, where $d$ is the diameter and $r$ is the radius. Area of a Circle: $A = pi r^2$, where $r$ is the radius. This gives the total space inside the circle. Arc Length and Area of a Circle Sector: […]
Perpendicular and Parallel Lines
? Video Tutorial Definitions of Line Types: Line segments have two endpoints, rays have one, and lines extend infinitely. Perpendicular Lines: Intersect at a 90-degree angle. Parallel Lines: Remain the same distance apart and never intersect. Measuring Distance: Between two points, from a point to a line (using a perpendicular line), and between parallel lines. […]