About this worksheet

This free Year 8 Pythagoras’ theorem shorter side worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MMGTW3. It targets one skill so students can practise until it sticks: by the end, students can say “I can rearrange Pythagoras’ theorem to find a shorter side and decide whether to add or subtract.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Rearranging Pythagoras' theorem to find a shorter side
• Deciding whether to add or subtract squares
• Finding heights of isosceles triangles

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 58, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Adding squares when finding a shorter side
• Subtracting the larger square from the smaller
• Using the full base instead of half in an isosceles triangle
• Getting a shorter side longer than the hypotenuse

Where this fits in the WA Year 8 sequence

Pythagoras’ Theorem: Finding a Shorter Side sits in the Two-dimensional space and structures sub-strand of Measurement and geometry. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Adding squares when finding a shorter side
• Subtracting the larger square from the smaller
• Using the full base instead of half in an isosceles triangle
• Getting a shorter side longer than the hypotenuse