Geometry proofs

Some of the most important geometry proofs are demonstrated here. I will provide you with solid and thorough examples.

Observations, measurements, and experimentations are not proof

If a formula works for 1 million specific examples, this is still not a proof

Understanding a proof can be a daunting task. Writing a proof can even be more daunting

I kept the reader(s) in mind when I wrote the proofs outlines below.

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

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Area of shapes proofs

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.

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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

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Proofs related to angles

Vertical angles theorem proof
See a proof of the vertical angles theorem.

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.