Question

How can we find a perimeter of a triangle using mid-point theorem? ​

Answer 1

Answer:

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 the 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.

MidPoint Theorem Statement

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Example:

In triangle ABC, the midpoints of BC, CA, AB are D, E, and F respectively. Find the value of EF, if the value of BC = 14 cm

Solution:

Given: BC = 14 cm

If F is the midpoint of AB and E is the midpoint of AC, then using the midpoint theorem:

EF = 1/2 (BC)

Substituting the value of BC,

EF = (1/2) × 14

EF = 7 cm

Therefore, the value of EF = 7cm.

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