What is Morleys theorem?

Morley’s theorem states that if ABC be any triangle, and if those trisectors of the angles B and C adjacent to BC meet in L, and M, N be similarly constructed, then the triangle LMN is equilateral.

What is a Trisector of a triangle?

In plane geometry, Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley.

What is Napoleon’s theorem used for?

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle.

How do you prove Thales Theorem?

Proof on Thales theorem : If a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio. Given : In ∆ABC , DE || BC and intersects AB in D and AC in E. Construction : Join BC,CD and draw EF ┴ BA and DG ┴ CA.

What is in the scalene triangle?

A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.

Why Trisecting the angle is impossible?

Since an arbitrary angle can’t be trisected, and we can’t find any integer angles except multiples of three degrees, Therefore you cannot construct an exact one-degree angle with ruler and compass!

How do you construct Napoleon’s triangle theorem?

Step 1: Construct a midpoint for each side of the triangles. Step 2: Construct a segment connecting the midpoint of a side of the equilateral triangle to the opposite vertex. Do this for each midpoint, creating three segments. The point of intersection is the center of the equilateral triangle.

Which theorem is known as Thales theorem?

basic proportionality theorem
The intercept theorem, also known as Thales’s theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.