Geometry Formal Proof Example

Introduction:
                     The word “geometry” is derived from the grouping of two Greek words “Geo” and “me tron”. The word “Geo” means “earth” and “me tron” means “measurement”. Thus subject is called as “earth measurement”. It was originally named as “geometry”.
                     In the early improvement of this subject, Egyptians applied geometrical principles in surveying and construction of temples, tombs and pyramids. Later, Greeks emphasized the logical reasoning of geometrical information and they dedicated their knowledge on geometry to the world of mathematics through the works of Pythagoras and Euclid. The Geometry formal proof examples are given below.

Geometry Formal Proofs Examples:

Example 1. The angles opposite to equal sides of a triangle are equal.
      Given: ABC is a triangle where AB = AC (see Figure)

      To prove: ∠B = ∠C.
      Construction: Mark the mid point of BC as M and join AM.
      Proof: In the triangles AMB and AMC
      (i) BM = CM (ii) AB = AC (iii) AM is common.
          By the SSS criterion, ΔAMB ≡ ΔAMC.
          Corresponding angles are equal. In particular, ∠B = ∠C.
          Hence the theorem is proved