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
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.
Proofs related to triangles
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
Proofs related to angles
Vertical angles theorem proof
See a proof of the vertical angles theorem.
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