The text, Pythagoras’ Theorem, begins by explaining what is meant by the hypotenuse of a right-angled triangle and explains how Pythagoras’s Theorem shows a connection between the areas of the squares drawn on each side of the right-angled triangle. There follows simple, straightforward examples and exercises to consolidate understanding of the underlying principles of Pythagoras’s Theorem. The next section contains explanations, examples and exercises finding the length of the hypotenuse in a variety of situations before moving on to require the students to find the length of one of the other sides of the triangle.
More complex examples covered include finding the length of the sides of an isosceles right-angled triangle when the length of the hypotenuse is given. Students then solve problems in a variety of different contexts including problems where they are required to draw an appropriate diagram. The final section explains how Pythagoras’s Theorem can be used to identify whether a triangle is right angled, acute angled or contains an obtuse angle.
The activities sheet contains an activity in which students work through Bronowski’s proof of Pythagoras’s Theorem, explore the areas of squares on the sides of a right-angled triangle, investigate the length of the perpendicular height of an equilateral triangle and investigate Pythagorean triples.