Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving

problem

Triangle in a square

Age

7 to 11

Challenge level

Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?

problem

Diagonally square

Age

7 to 11

Challenge level

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

problem

Proof sorter - circumference angles

Age

11 to 16

Challenge level

problem

The converse of pythagoras

Age

14 to 18

Challenge level

Can you prove that triangles are right-angled when $a^2+b^2=c^2$?

problem

Circumference angles

Age

11 to 16

Challenge level

Can you prove the angle properties described by some of the circle theorems?

problem

Cyclic quadrilaterals proof

Age

11 to 16

Challenge level

Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?

problem

Mathdoku

Age

7 to 11

Challenge level

Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?

problem

Unravelling sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?

problem

Difference of odd squares

Age

14 to 18

Challenge level

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?

problem

Impossible sums

Age

14 to 18

Challenge level

Which numbers cannot be written as the sum of two or more consecutive numbers?

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For younger learners

Reasoning, convincing and proving

Triangle in a square

Diagonally square

Proof sorter - circumference angles

The converse of pythagoras

Circumference angles

Cyclic quadrilaterals proof

Mathdoku

Unravelling sequences

Difference of odd squares

Impossible sums