# Pythagoras’ Theorem

## Key Stage 3: Year 8: Term 6: Pythagoras’ Theorem

Students are guided by discovering Pythagoras’ Theorem and learn how to apply it to calculate an unknown side in a right-angled triangle. As learning progresses, they connect Pythagoras’ Theorem to other areas of mathematics and use it to solve real-life problems.

This unit takes place in Year 8 Term 6 and is follows finding the area of 2D and 3D shapes.

4 Part Lesson
4 Part Lesson
4 Part Lesson
4 Part Lesson
##### Calculating the Hypotenuse in a right-angled triangle
Extended Learning
Problem Solving
Revision
##### Prerequisite Knowledge
• Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon
##### Key Concepts
• For a right-angled triangle, Pythagoras’ Theorem states that a2 +b2 = c2 where c is the hypotenuse.
• A Pythagorean triple is a set of three integers that exactly fits the Pythagoras relationship.
• If the lengths of the three sides of a triangle obey Pythagoras’ Theorem the triangle is right-angled.
• Students should look for right-angled triangles in shapes with problem solving with Pythagoras’ Theorem.
##### Working mathematically

Develop fluency

• Use language and properties precisely to analyse 2-D and 3-D shapes.
• Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
• Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

• Make and test conjectures about patterns and relationships; look for proofs or counter-examples
• Begin to reason deductively in geometry, number and algebra, including using geometrical constructions

Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Develop their use of formal mathematical knowledge to interpret and solve problems
• Begin to model situations mathematically and express the results using a range of formal mathematical representations
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems
##### Subject Content

Geometry and measures

• Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
• Use Pythagoras’ Theorem in similar triangles to solve problems involving right-angled triangles
• Interpret mathematical relationships both algebraically and geometrically.

### Mr Mathematics Blog

#### Volume of Similar Shapes

In this lesson, we learn about the length and volume scale factor of 3D shapes and the relationship between them.