Module 1

• Exterior Angle Inequality Theorem


  • The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
• Hinge Theorem


  • If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second
• The largest angle of a triangle is opposite to the longest side
• The smallest side of a triangle is opposite to the smallest angle
• The sum of any two sides of a triangle is greater than the third side
• Ruel cannot form a triangle with the given stick lengths of 8 in, 8 in, 8 in
• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written


  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by

  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by

  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility

  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• L

  Side of triangle
• L is greater than the opposite side of ∠E

  L is longer than the opposite side of ∠E
• Hinge Theorem or SAS Inequality Theorem


  If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second
• Hinge devices


  • Used to fasten or join two things together and allow adjustment, rotation, twisting or pivoting
• Hinge devices

  • Doors, scissors, compass, folding ladder
• Angle of scissors opening

  Larger angle corresponds to wider opening
• Converse of Hinge Theorem or SSS Inequality Theorem


  If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second
• Theorems in triangle inequalities

  • Angle-Side Relationship
  • Triangle Inequality Theorem
  • Exterior Angle Inequality Theorem
  • Hinge Theorem or SAS Inequality Theorem
  • Converse of Hinge Theorem or SSS Inequality Theorem