Question

Hard Question :-

⭐ What is midpoint theorem ? explain deeply

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Answer 1

Geometry is one among the significant and essential branches of mathematics. This field deals with the geometrical problems and figures which are based on their properties. One of the important theorems in the field of geometry that deals with the properties of triangles are called the Mid- Point Theorem.

Geometry is one among the significant and essential branches of mathematics. This field deals with the geometrical problems and figures which are based on their properties. One of the important theorems in the field of geometry that deals with the properties of triangles are called the Mid- Point Theorem.The theory of midpoint theorem is used in coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. Both the ‘x’ and the ‘y’ coordinates must be known for solving an equation using this theorem. The Mid- Point Theorem is also useful in the fields of calculus and algebra.

Answer 2

$\huge{\bf{\underline{\red{Answer :}}}}$

The midpoint theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side. Whereas, its converse states that the line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

$\huge{ \mathfrak{ \underline{Formula:-}}}$

(xₘ , yₘ) = $\large( \frac{x_1 +x_2}{2} , \frac{y_1 +y_2}{2} )$

(xₘ , yₘ) = Coordinates of the midpoint

(x₁ , y₁) = Coordinates of the First point

(x₂ , y₂) = Coordinates of the Second point