Lessons
16Triangles and Pythagoras
Solve problems involving unknown sides and angles in triangles using known properties and the theorem of Pythagoras.
The Theorem of Pythagoras
Investigate the relationship between the lengths of the sides of a right-angled triangle and develop the Theorem of Pythagoras.
Working with the Theorem of Pythagoras
Calculate unknown sides of right-angled triangles - finding the hypotenuse and the legs - and leave answers in surd form where needed.
The Converse of the Theorem of Pythagoras
Determine whether a triangle is right-angled, obtuse-angled or acute-angled using the converse of the Theorem of Pythagoras.
Applications of the Theorem of Pythagoras
Solve real-world problems - shortest routes, ladders, screens and braces - using the Theorem of Pythagoras.
Area and Perimeter of Circles
Use pi to calculate the circumference and area of circles, and describe the relationships between radius, diameter, circumference and area.
Area of Polygons by Decomposition
Calculate the areas of polygons by decomposing them into rectangles and triangles, including using the Theorem of Pythagoras to find missing heights.
Perimeter and Area of Composite Figures
Solve perimeter and area problems for composite figures made from rectangles, triangles, circles and parts of circles, and convert between SI units.
Composite Figures and Unit Conversions
Follow a structured problem-solving strategy to calculate perimeters and areas of composite figures with polygons and circles, and convert between SI units, squaring the scale factor for square units.
Classifying Triangles
Identify and classify triangles by their sides and angles: equilateral, isosceles, scalene, right-angled, acute and obtuse.
Investigating the Interior Angles of a Triangle
Investigate and prove that the interior angles of any triangle add up to 180 degrees, and calculate unknown angles.
Investigating the Size of Angles in an Equilateral Triangle
Establish that every interior angle of an equilateral triangle is 60 degrees and use this to solve problems.
Classifying Quadrilaterals
Identify and classify quadrilaterals - square, rectangle, rhombus, parallelogram, trapezium and kite - using sides, angles and parallel lines.
Solving Problems in Triangles: Unknown Angles and Sides
Solve for unknown angles and sides in triangles using angle properties, parallel lines and the theorem of Pythagoras, with reasons.
Solving Problems in Quadrilaterals
Solve for unknown angles in quadrilaterals using the 360 degree angle sum and the properties of parallelograms and trapeziums, with reasons.
Congruent and Similar Shapes
Identify, describe and verify congruent and similar shapes using corresponding angles and side ratios.