Geometry proofs
Some of the most important geometry proofs are demonstrated here. I will try to provide you with solid and thorough examples.
Observations, measurements, and experimentation are not proofs. If a formula works for 1 million specific examples, this is still not a proof.
My approach is to explain everything at the same time I am writing the proof. If you are interested in proofs, you will find the proofs below a pleasure to read.
Reasoning and proof
Geometry proofs related to area of shapes.
Proof of the area of a circle
Here, we prove that the area of a circle is pi × r2 by inscribing circles into polygons.
Proof of the area of a triangle
A crystal clear proof of the area of a triangle. We will know why it makes sense to multiply the base by the height and divide the result by two.
Proof of the area of a parallelogram
Here, we prove that the area of a parallelogram is base times height by turning a parallelogram into a rectangle.
Proof of the area of a trapezoid
Here, we prove that the area of a trapezoid is the average of the two parallel bases times the height by turning a trapezoid into a rectangle.
Here, we prove that the area of a circle is pi × r2 by inscribing circles into polygons.
Proof of the area of a triangle
A crystal clear proof of the area of a triangle. We will know why it makes sense to multiply the base by the height and divide the result by two.
Proof of the area of a parallelogram
Here, we prove that the area of a parallelogram is base times height by turning a parallelogram into a rectangle.
Proof of the area of a trapezoid
Here, we prove that the area of a trapezoid is the average of the two parallel bases times the height by turning a trapezoid into a rectangle.
Geometry proofs related to triangles
Proof of the triangle midsegment theorem
A crystal clear proof of the triangle midsegment theorem.
Proof of the angle sum theorem
A crystal clear proof of the angle sum theorem.
Triangle inequality theorem proof
A crystal clear proof of the triangle inequality theorem.
Base angles theorem proof
A crystal clear proof of the base angles theorem.
Right isosceles triangle
Prove that the median of a right isosceles triangle is half the hypotenuse.
A crystal clear proof of the triangle midsegment theorem.
Proof of the angle sum theorem
A crystal clear proof of the angle sum theorem.
Triangle inequality theorem proof
A crystal clear proof of the triangle inequality theorem.
Base angles theorem proof
A crystal clear proof of the base angles theorem.
Right isosceles triangle
Prove that the median of a right isosceles triangle is half the hypotenuse.
Geometry proofs related to angles
Geometry proofs related to quadrilaterals
Prove that opposite sides of a parallelogram are congruent
See how to prove that opposite sides of a parallelogram are equal.
Prove that the diagonals of a rectangle are congruent
See how to prove that the diagonals of a rectangle are equal.
Prove that the diagonals of a trapezoid are congruent
See how to prove that the diagonals of a trapezoid are equal.
Prove that the diagonals of a kite are perpendicular
See how to prove that the diagonals of a kite are perpendicular.
See how to prove that opposite sides of a parallelogram are equal.
Prove that the diagonals of a rectangle are congruent
See how to prove that the diagonals of a rectangle are equal.
Prove that the diagonals of a trapezoid are congruent
See how to prove that the diagonals of a trapezoid are equal.
Prove that the diagonals of a kite are perpendicular
See how to prove that the diagonals of a kite are perpendicular.
