Mathematics

Proving the Law of Sines

If you understand the definition of sine, it is pretty easy to prove the "Law of Sines".

Mathematics

Proving the Law of Sines

If you understand the definition of sine, it is pretty easy to prove the "Law of Sines".

Mathematics

Proving Alternate Interior Angles are Congruent (the same)

The Alternate Interior Angles Theorem states that If two parallel straight lines are intersected by a third straight line (transversal), then the angles inside (between) the parallel lines, on opposite sides of the transversal are congruent (identical). This is illustrated in the image below: We see two parallel lines and a third line (transversal) intersecting […]

Mathematics

Proving that the Angles in a Triangle Sum up to 180°

Proving that the angles inside a triangle – any triangle – sum up to 180° is very simple, but leaves most people unsatisfied (or unconvinced) because it depends on the properties of something called Alternate Interior Angles. I’ll give the proof first and then explain Alternate Interior Angles A demonstration of the angles of a […]

Mathematics

Proving the Pythagorean Theorem

We learned the Pythagorean Theorem in grade school: The square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Often written as A2 + B2= C2. The Pythagorean Theorem is much more than just a mathematical curiosity, it is a basic and useful mathematical property […]