The Pythagorean theorem – Grade 10 math lesson

Lesson 9 of 16 in the Grade 10 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 10 (ages 15–16)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “How can builders use a 3-4-5 triangle to check a right angle?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Adding when finding a shorter side. If you want a short side, subtract from the hypotenuse squared.
Forgetting to square root at the end. Check: the hypotenuse must be the longest side.

Tip for home: Work out the length of a ladder needed to reach a window.

What your child will learn

Learning goal: use Pythagoras' theorem to find missing sides in right-angled triangles.

Success looks like

I can find the hypotenuse.
I can find a shorter side.
I can use Pythagoras in problems.

Key words

hypotenuse: the longest side, opposite the right angle
right angle: an angle of 90°
square root: the number that squares to give the value
converse: if a² + b² = c², the angle is a right angle

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Use a 3, 4, 5 triangle made from string to check right angles in the corner of a room.

The big ideas (for the adult)

In a right triangle, a² + b² = c², where c is the hypotenuse, the longest side opposite the right angle.

To find the hypotenuse, square the two shorter sides, add, then square root. To find a shorter side, subtract instead.

Use it to find distances between points on a grid and to check whether a triangle has a right angle.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

Geometry: Right Triangles and Trigonometry Practice TestGraded instantly

All Grade 10 math lessons and tests · Math Department

More Grade 10 math lessons

Curriculum

Common Core State Standards HSG.GPE.B.7: “Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*”

Common Core State Standards 8.G.B.8: “Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.