AI generatedGeometry and measuresKey Stage 3

Checking whether a triangle is right-angled

Checking whether a triangle is right-angled.

  • The hypotenuse is the longest side and lies opposite the right angle.
  • To test a triangle, compare the square of its longest side with the sum of the other two squares.

Example 1

A triangle has sides 3 cm, 4 cm and 5 cm. Is it right-angled? Show a check.

Square and add the two shorter sides.Compare with the square of the longest side.
Yes, because .

Example 2

A triangle has sides 4 cm, 3 cm and 6 cm. Is it right-angled? Show a check.

Square and add the two shorter sides.Compare with the square of the longest side.
No, because the two results are different.

Your turn

Question 1

A triangle has sides 5 cm, 12 cm and 13 cm. Is it right-angled? Show a check.

Check answer
Square and add the two shorter sides.Compare with the square of the longest side.
Yes, because .
Question 2

A triangle has sides 12 cm, 5 cm and 14 cm. Is it right-angled? Show a check.

Check answer
Square and add the two shorter sides.Compare with the square of the longest side.
No, because the two results are different.
Question 3

A triangle has sides 8 cm, 15 cm and 17 cm. Is it right-angled? Show a check.

Check answer
Square and add the two shorter sides.Compare with the square of the longest side.
Yes, because .
Question 4

A triangle has sides 15 cm, 8 cm and 18 cm. Is it right-angled? Show a check.

Check answer
Square and add the two shorter sides.Compare with the square of the longest side.
No, because the two results are different.
Question 5

A triangle has sides 7 cm, 24 cm and 25 cm. Is it right-angled? Show a check.

Check answer
Square and add the two shorter sides.Compare with the square of the longest side.
Yes, because .
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