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Shape and Space Unit 1:
Angles and Triangles

An angle is the figure formed by two line segments that extend from a common point. We can measure the size of an angle by the amount of rotation required to superimpose one line segment on the other. The importance of such a simple concept and its applications in real-life cannot be over-estimated.
Angles have long been used to tell the time through sundials, to calculate the position of the planets and stars and to determine the best route to follow at sea by ocean liners. In today’s world, they play a crucially role in the construction of new buildings (ever heard of a theodolite ? what about a spirit-level ?), when aircraft make their final descent, or in sport if you want to become a record-breaking Javelin thrower or you need to design the steering in a rally car.

A triangle is a closed plane figure bounded by three straight lines meeting at 3 vertices. It is the simplest shape with the smallest possible number of straight sides. The ancient Greeks quickly latched on to the power of this shape when they constructed their pyramids, but nowadays, triangles are essential for the construction of maps, for the simulation of images in computer graphics (using triangular meshes), for GPS satellite navigation and even by some animals in the pursuit of food.

Unit 1.1: Parallel lines.
Unit 1.2: Identifying congruent triangles.
Unit 1.3: Working with similar triangles.
Unit 1.4: Finding the area of a triangle.
Unit 1.5: Proving some triangle results.
Unit 1.6: Finding angles in polygons.

Learning Objectives

In this unit the student will be able to

  • Identify equivalent angles when two lines are parallel.
  • Recognise congruent triangles.
  • Calculate the lengths of sides when two triangles are similar.
  • Appreciate the formula for the area of a triangle.
  • Calculate the area of some simple shapes.
  • Explain why the sum of angles in a triangle is 180 degrees.
  • Calculate angles in polygons.

 

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