# Pythagoras' Theorem

This resource package is to support the teaching and learning of Pythagoras' Theorem

KS3: Use **Pythagoras' Theorem** and side ratios in similar triangles to solve problems in right-angled triangles.

KS4: apply trigonometric ratios, sine and cosine rules, and **Pythagoras’s theorem** in two and three dimensions

### Teaching Pythagoras

A fifteen minute video for teacher use as inspiration when planning an introduction to Pythagoras' Theorem to key stage three students.

(This video could be used in departmental discussion when planning the approach Pythagoras for students of different ability level)

### Pythagoras' Theorem

This is an ideal example of a resource which could be used in planning sessions to highlight which approaches should be used for different ability students. There are also a number of activities which could be used as extension work. Ideal to link this resource to several places in the scheme of work highlighting which activities are to be used, how they should be used and highlight the opportunities to develop fluency, problem solving...

### Pythagoras' Theorem

The text is a good source of straight forward questions useful for consolidation. Page 16 has questions requiring students to identify which triangles are right angled. Students should experience **problems in context. **Examples begin on page 12.

Question 10 on page 18 is a good extension question.

### Task Maths 4

**Tilted Squares Activity** (Chapter 10 page 11 of part 2)

This activity is to be used in key stage four to reintroduce Pythagoras' Theorem. Opportunity to bring in many mathematical topics.

Begin by asking how we can **calcuate** the length of the vector (4¦3) Discuss the difference between calculate and measure. Explore the link between the area of a square and the length of a side of a square. Explore different methods for finding the area of a tilted square. Emphasise that a clear description of the method of finding the area of the square is what is required.

At this point begin the tilted square activity. The aim is to re-enforce that Pythagoras' Theorem is as much to about areas of squares as it is about right-angled triangles.

**Extension **(p. 153 of book, p 15 of the pdf) Q5 area of isosceles triangle, Q7 proof using Pythagors' theorem, Q8 Is Pythagors' Theorem still valid for non right-angles triangles?

**Further exension** (Page 155) Does Pythagoras Rule work with other shapes other than squares e.g semi-circles?

### You Tube Video of Proof of Pythagoras' Theorem

Ask students to attempt to proof Pythagoras' Theorem. Give them plenty of time ty a few different approaches. Students who succeed could be given the opportunity to make a brief video for upload on to Youe Tube.

For students who require some scaffolding, begin to play the video. Stop the video after 45 seconds.

Note there are many proofs of Pythagoras Theorem so do not lead students to this particular proof unless they require help. Once they are happy with this proof challenge them to fin d a different proof.