What is Thales theorem in triangle?

The basic proportionality theorem, also known as the Thales theorem states that “the line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion”.

What were Thales 5 theorems of elementary geometry?

In particular, he has been credited with proving the following five theorems: (1) a circle is bisected by any diameter; (2) the base angles of an isosceles triangle are equal; (3) the opposite (“vertical”) angles formed by the intersection of two lines are equal; (4) two triangles are congruent (of equal shape and size …

How do you prove Thales theorem in a triangle?

How to Solve the Thales Theorem?

1. To prove the Thales theorem, draw a perpendicular bisector of ∠
2. Let point M be the midpoint point of line AC.
3. Also let ∠MBA = ∠BAM = β and ∠MBC =∠BCM =α
4. Line AM = MB = MC = the radius of the circle.
5. ΔAMB and ΔMCB are isosceles triangles.

Can a triangular Pentagon be an equable rectangular Pentagon?

For a convex rectangular pentagon, the base angles of the triangular portion must be acute. Thus, if the triangle is obtuse or right, then only its longest side can be the base. By convention, the area of an equable rectangular pentagon is an integer, as is that of its rectangular portion, so by subtraction the triangle is Heronian.

Is the triangle PQR always a right triangle?

In the figure above, no matter how you move the points P,Q and R, the triangle PQR is always a right triangle, and the angle ∠PRQ is always a right angle. A practical application – finding the center of a circle

How are the sides of a triangle related?

Triangles are named by their vertices: The triangle in Figure 3.5.1 is called △ABC. Figure 3.5.1: Triangle ABC has vertices A, B, and C. The lengths of the sides are a, b, and c. The three angles of a triangle are related in a special way. The sum of their measures is 180 ∘. Note that we read m∠A as “the measure of angle A.”

What are the internal angles of the ∆ABC triangle?

The three internal angles of the ∆ABC triangle are α, ( α + β ), and β. Since the sum of the angles of a triangle is equal to 180°, we have ∴ α + β = 90 ∘ . {\\displaystyle herefore \\alpha +\\beta =90^ {\\circ }.} Q.E.D. {\\displaystyle C= (1,0)} . Then B is a point on the unit circle {\\displaystyle (\\cos heta ,\\sin heta )} .