Mid-Point Theorem Converse
The line drawn through the mid-point of one side of a triangle parallel to the base of a triangle bisects the third side of the triangle.
Given:
In triangle PQR, S is the mid-point of PQ and ST ∥ QR
To Prove:
T is the mid-point of PR.
Construction:
Draw a line through R parallel to PQ and extend ST to U.
Proof:
ST∥ QR (given)
So, SU∥ QR
PQ∥ RU (construction)
Therefore, SURQ is a parallelogram.
SQ = RU (Opposite sides of parallelogram)
But SQ = PS (S is the mid-point of PQ)
Therefore, RU = PS
In △PST and △RUT
∠1 =∠2 (vertically opposite angles)
∠3 =∠4 (alternate angles)
PS = RU (proved above)
△PST ≅ △RUT by AAS criteria
Therefore, PT = RT
T is the mid-point of PR.
Mid Point Theorem
Midpoint theorem states that “The line segment drawn from the midpoint of two sides of the triangle is parallel to the third side and is equal to half of the third side of the triangle. Geometry is an important part of mathematics that deals with different shapes and figures. Triangles are an important part of geometry and the mid-point theorem points towards the midpoints of the triangle.
Table of Content
- What is the Midpoint Theorem?
- Mid Point Theorem Definition
- Mid-Point Theorem Proof
- Mid-Point Theorem Converse
- Mid Point Formula
- Examples on Mid Point Theorem