Start with the claim and the givens
Write what is known and what you need to show. A useful proof connects them through definitions, accepted results, and justified deductions rather than through a series of measurements from a drawing.
Make each reason visible
Explain why two angles are equal, why a total is 180°, or why an equation follows. A short chain with an explicit reason at each step is stronger than a long calculation with an unsupported assumption.
A mistake to avoid
Testing a few drawings does not prove a general geometric statement. Also avoid assuming the conclusion itself while trying to justify it.
Worked example
Find the base angles of an isosceles triangle
Given AB = AC and angle A = 40°, the base-angle theorem gives angle B = angle C. The triangle angle sum gives B + C = 140°. Equal angles sharing that total are 70° each. The equality comes from the stated equal sides, not from how the triangle looks.