# Inscribe Angle Theorem

Below are the tutorials on Inscribe Angle Theorem. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: INSA1 Introduction to the Inscribed Angle Theorem Series

Lesson 2: INSA2 Inscribed and Central Angles Intercepting the Same Arc

Lesson 3: INSA3 Proof of the Inscribed Angle Theorem (Case 1)

Lesson 4: INSA4 Proof of the Inscribed Angle Theorem (Case 2)

Lesson 5: INSA5 Proof of the Inscribed Angle Theorem (Case 3)

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# Angle Sum Tutorial Series

Below are the tutorials on Angle Sum Theorem. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

# Proof of Sum of the Exterior Angles of a Polygon

After proving that the sum of the interior angles of a polygon is 180(n-2), where n is the number of sides, let us now prove that the sum of the exterior angles is 360 degrees. The exterior angle of a polygon is the angle formed after extending one side of a polygon. It is the supplementary of the adjacent interior angle.

The proof uses the polygon angle sum theorem.

# The Polygon Angle Sum Proof

The video above shows why the formula for the sum of the interior angles of a polygon with n sides is equal to $180(n-2)$. The polygon angle sum theorem shows the relationship between the number of sides of a polygon and the sum of its interior angles. The expression $n - 2$ is the maximum number of triangles that can be formed in a polygon by drawing  non-overlapping diagonals. The video above was labeled as a conjecture because the assumption is that it has not been proven that $n - 2$ is indeed the number of triangles for all polygons with $n$ sides. If we make this assumption is true, then the conjecture in the video becomes a proof.

# Proof that the Quadrilateral Angle Sum is 360 Degrees

After discussing the triangle angle sum proof, we now discuss the quadrilateral angle sum proof. The proof of this theorem comes from the fact that we can divide a quadrilateral into two triangles by drawing a diagonal. Since each triangle angle sum is 180°, the sum of the interior angle of the quadrilateral is therefore 360°.

Watch the video above to know the details of its proof.

# Proof That Square Root of 2 is Irrational

Rational numbers are numbers that can be expressed as fractions and hence can be expressed as $\frac{a}{b}$ where $a$ and $b$ are integers and $b$ not equal to 0. All rational numbers can be expressed as lowest terms. These are some of the important things to consider in proving that square root of 2 is irrational.

In proving the theorem, you also should be familiar with proof by contradiction. This proof method requires the negative assumption of statement that you are trying to prove, and then, finding a contradiction along the proof. When this happens, then your assumption must be false and hence the statement that you are trying to proof is true. You will need to study this concept for you to understand the proof.