Success TutoringWorksheets
Download Free PDF
Study GuideYear 9Level 2 · Standard

Free Year 9 Pythagoras' Theorem Explained

Explains Pythagoras' theorem for right-angled triangles, how to find the hypotenuse, how to find a shorter side, and how to test whether a triangle is right-angled. Worked examples include exact answers, rounded answers and a practical ladder problem.

Download Free PDF

Instant download · No sign-up · Free for personal, classroom and homeschool use

Year
Year 9
Subject
Mathematics
Topic
Pythagoras' Theorem
Difficulty
Level 2 · Standard
Estimated time
20 minutes
Curriculum
Australian Curriculum
Answers
Not applicable
Format
PDF (A4) + print

Students will practise

  • understanding the relationship c[sup 2] = a[sup 2] + b[sup 2] in a right-angled triangle
  • identifying the hypotenuse
  • finding the hypotenuse and a shorter side
  • testing whether a triangle is right-angled

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Pythagoras' Theorem Explained

  1. 1Year 9 Pythagoras' Theorem Worksheet — Level 1
  2. 2Year 9 Pythagoras' Theorem Worksheet — Level 2
  3. 3Trigonometry Cheat Sheet: SOH CAH TOA
  4. 4Year 9 Trigonometry (Finding Sides) Worksheet — Level 1
Study guide

How to use this study guide

  1. Read it together first, pausing at each worked example to try the step before reading the answer.
  2. Attempt the "Check yourself" questions at the end without looking back.
  3. Then practise with a worksheet from the pathway above and finish with the topic test.

Common questions

Who is this study guide for?

Year 9 students (typically ages 14–15) working on pythagoras' theorem. It is pitched at level 2 · standard.

Are the answers included?

This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.

How long does it take?

About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try Year 9 Pythagoras' Theorem Worksheet — Level 1.

Preview

Year 9 · Mathematics · Pythagoras' Theorem

Pythagoras' Theorem Explained

Success Tutoring

Student name:

Date:

What you need to know

In a right-angled triangle, the longest side is called the hypotenuse. It is always opposite the right angle. Pythagoras' theorem says that the square of the hypotenuse equals the sum of the squares of the other two sides: c[sup 2] = a[sup 2] + b[sup 2], where c is the hypotenuse and a and b are the two shorter sides. The theorem only works for right-angled triangles.

Finding the hypotenuse (shorter sides 6 and 8)

  1. c2 = 62 + 82
  2. c2 = 36 + 64 = 100
  3. c = √100 = 10

Finding a shorter side (hypotenuse 13, one side 5)

  1. Rearrange: b2 = c2 − a2.
  2. b2 = 132 − 52 = 169 − 25 = 144
  3. b = √144 = 12

When the answer is not a whole number (shorter sides 4 and 7)

  1. c2 = 42 + 72 = 16 + 49 = 65
  2. c = √65. This is the exact answer.
  3. As a decimal, c ≈ 8.06 (to 2 decimal places). Leave the answer as √65 unless the question asks you to round.
Common mistake: adding the squares when finding a shorter side. If you are given the hypotenuse, you must subtract. A quick sanity check: the hypotenuse must come out as the longest side.

Is the triangle right-angled?. The theorem works in reverse too. If the longest side squared equals the sum of the other two sides squared, the triangle is right-angled. If not, it is not.

Sides 7, 24 and 25

  1. Longest side is 25: 252 = 625.
  2. 72 + 242 = 49 + 576 = 625.
  3. The two results match, so the triangle is right-angled.
Pythagorean tripleCheck
3, 4, 59 + 16 = 25
5, 12, 1325 + 144 = 169
8, 15, 1764 + 225 = 289
7, 24, 2549 + 576 = 625
6, 8, 10 (3, 4, 5 doubled)36 + 64 = 100
Recognising the common triples saves time: any multiple of a triple (such as 9, 12, 15) is also a right-angled triangle.

A 5 m ladder leans against a wall with its foot 3 m from the wall. How high up the wall does it reach?

  1. The ladder is the hypotenuse (5 m), the ground distance is one shorter side (3 m) and the height is the other shorter side (h).
  2. h2 = 52 − 32 = 25 − 9 = 16
  3. h = √16 = 4 m

Check yourself

  1. Shorter sides 9 and 12. Find the hypotenuse.
  2. Hypotenuse 10, one shorter side 6. Find the other side.
  3. Shorter sides 5 and 5. Find the hypotenuse to 2 decimal places.
  4. Is a triangle with sides 6, 8 and 11 right-angled?
  5. Hypotenuse 17, one shorter side 8. Find the other side.
  6. Shorter sides 2 and 3. Find the hypotenuse, exact and to 2 decimal places.

Answers: 1. 15 2. 8 3. √50 ≈ 7.07 4. No (36 + 64 = 100, but 112 = 121) 5. 15 6. √13 ≈ 3.61

worksheets.successtutoring.com · Free to print and share for personal and classroom use

Preview — the PDF contains the full resource.

More Year 9 pythagoras' theorem resources

  • Worksheet

    Year 9 Pythagoras' Theorem Worksheet — Level 1

    Find the hypotenuse or a shorter side of a right-angled triangle. Builds confidence with the core skill before adding complexity. This…

    Difficulty
    Level 1 · Easier
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included
  • Worksheet

    Year 9 Pythagoras' Theorem Worksheet — Level 2

    Find the hypotenuse or a shorter side of a right-angled triangle. Expected-level practice for this year group. This Year 9 worksheet has 8…

    Difficulty
    Level 2 · Standard
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included
Was this resource helpful?

About this resource

Created by
Success Tutoring
Last reviewed
1 October 2026
How it was made
Written by our team

Free to print and share for personal, classroom and homeschool use. Please don't resell. Spotted an error? Let us know.