Pythagoras' Theorem: Triangles Within Triangles WORKSHEET
Suitable for Year groups: Year 9, Year 10
GCSE Tier: Foundation/Higher
Targeting grades: 4-5
Prerequisite knowledge: Pythagoras’ Theorem. Identifying right-angled triangles. Substituting and solving for unknown sides. Basic algebraic manipulation.
Pythagoras' Theorem: Triangles Within Triangles WORKSHEET DESCRIPTION
Take Pythagoras’ Theorem to the next level with this Triangles Within Triangles worksheet. Students move beyond simple right-angled triangles to find missing lengths in diagrams where multiple triangles share sides or overlap.
The first two questions guide learners to calculate a required hypotenuse by first finding two other side lengths, reinforcing a structured, step-by-step approach. The final question introduces similar triangles, challenging pupils to apply a scale factor of enlargement to reach the solution. Throughout the worksheet, students identify common sides, infer perpendiculars, and form equations methodically, deepening both fluency and reasoning. To avoid rounding errors and confusion with exact values, the first calculation in each question uses a Pythagorean triple, ensuring that neat integer results carry through to later steps.
The first two questions guide learners to calculate a required hypotenuse by first finding two other side lengths, reinforcing a structured, step-by-step approach. The final question introduces similar triangles, challenging pupils to apply a scale factor of enlargement to reach the solution. Throughout the worksheet, students identify common sides, infer perpendiculars, and form equations methodically, deepening both fluency and reasoning. To avoid rounding errors and confusion with exact values, the first calculation in each question uses a Pythagorean triple, ensuring that neat integer results carry through to later steps.
