Pythagoras Theorem explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Pythagoras theorem is a rule for right triangles.
It connects the squares of the two shorter sides with the square of the longest side.
It is used in geometry, coordinate distance, construction, maps, ladders, and reaife measurement.
A right triangle has one angle of 90 degrees.
The hypotenuse is the side opposite the right angle. It is always the longest side of a right triangle.
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Pythagoras theorem says that the square of the hypotenuse equals the sum of the squares of the other two sides.
The theorem works only for right triangles.
Some side lengths, such as 3, 4, and 5, form a Pythagorean triplet because .
Meaning: A right triangle has one egree angle.
Definition: A right triangle is a triangle with one right angle.
Pythagoras theorem can be used only when the triangle has a right angle.
Meaning: The hypotenuse is the longest side of a right triangle.
Definition: The hypotenuse is the side opposite the right angle.
If the right angle is at B, the side across from B is the hypotenuse.
Meaning: The squares of the shorter sides add to the square of the hypotenuse.
Definition: In a right triangle, , where c is the hypotenuse.
If shorter sides are 6 and 8, , so .
Meaning: A shorter side can be found by subtraction.
Definition: If c is the hypotenuse, then missing side squarenown side squared.
If and one side is 5, missing side square, so missing sid.
Easy
Question: Find the hypotenuse of a right triangle with shorter sides 3 cm and 4 cm.
Medium
Question: A right triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the other side.
Exam-level
Question: Check whether 8 cm, 15 cm, and 17 cm can be sides of a right triangle.
Using the theorem for any triangle
Why it happens: The righngle condition is skipped.
Correct approach: Use Pythagoras theorem only for right triangles.
Choosing the wrong hypotenuse
Why it happens: The longest side is not identified.
Correct approach: The hypotenuse is opposite the right angle.
Adding when finding a shorter side
Why it happens: The formula is memorised without rearranging.
Correct approach: Subtract the known shorter side square from the hypotenuse square.
Can I use Pythagoras theorem without a right angle?
No. It applies only to right triangles.
Is the hypotenuse always the longest side?
Yes, in a right triangle.
What is a Pythagorean triplet?
It is a set of three whole numbers that satisfy .
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.
Meaning: Triplets are sets of three whole numbers that fit Pythagoras theorem.
Definition: A Pythagorean triplet has .
3, 4, 5 is a triplet because .