Pythagoras' Theorem

Learning Goal

Goal:  Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)

Timeframe: 4 lessons


Introduction

TASK 1

Watch the following videos.

What is Pythagoras' Theorem?







How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?






TASK 2

Login to Scootle and complete the Exploring the Pythagorean theorem learning object.

Link: http://www.scootle.edu.au/ec/pin/
PIN: YVSXTP


Exploration

TASK 3
Login to Scootle and complete the Exploring Square Roots learning object.  Complete the three items:
  • Square area and perfect squares
  • Square area
  • Complete the equations

For the Complete the equations activity, take a snap-shot (Shift-Command-4) of a completed equation.

Rename the file <Scootle - Pythagoras - username.png> and upload it to Google Drive > Maths > Pythagoras folder.

Link: http://www.scootle.edu.au/ec/pin/
PIN: LWNXCA

Assignment

TASK 4 - Due Fri 7 Mar 2014
Measure a wall in your house and calculate the largest 16:9 flat screen TV you could mount on that wall.

On an A4 piece of paper, draw the dimensions of the wall and show the calculations of how you worked out the biggest TV size (diagonal, in inches) you can mount.


An Example

Mr Flynn is considering buying a large LED TV for his games room.  The space available on the wall is 325cm wide and 180cm high.

Some things Mr Flynn will need to consider when making his calculations about the LED TV:

  • it has a width-to-height ratio of 16:9, so it might not fit exactly
  • the measurement will be in inches (not cm) and
  • it will be measured from one corner to the other (diagonal)

Think about how Mr Flynn will need to use similar triangles (and the ratio 16:9) to work out the greatest possible length and width of the TV.

Also, consider how will Mr Flynn use Pythagoras' Theorem to calculate the diagonal measurement of the TV.

Finally, how will Mr Flynn convert his measurement to inches.



Here is a step by step example of how Mr Flynn worked out his solution.


Skills

TASK 5

Login to Mathletics and complete the following four lessons in MG - Pythagoras and Trigonometry module:
  • Are You Ready?
  • Hypotenuse of a Right Triangle
  • Pythagoras' Theorem
  • Pythagorean Triads

Review

TASK 6

Add to your Maths Journal what you have learnt in this module.

Use diagrams, pictures, words, symbols and colour to express your learning.

Submit your Maths Journal when completed.


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