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.

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 outlined 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.

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.

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.

Geometry proofs related to angles

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

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.
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