Lesson Suggestions on giving a proof (for all students; not maths-major optimized)))

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When proving anything, there's something you must obey in order that it can be called a proof.
1. Make sure your proof follows RIGOROUS LOGIC. If you draw a conclusion C from conditions A and B, C must be completely based on A and B, and ONLY on A and B.
e.g.
Isosceles triangles have two equal sides
and
Triangle ABC is an isosceles triangle
∴Triangle ABC has two equal sides.

e.g.(wrong example)
Isosceles triangles have two equal sides
and
Triangle ABC is an isosceles triangle
∴AB=BC.

2. Make sure your proof is readable by everyone. Make everything obvious. Show with your best effort what conclusion is based on which condition(s). 
DO NOT SKIP MIDDLE STEPS in mind when proving. It's very likely you'll make mistakes-especially under time pressure in exams.

3. Make sure your proofs are based on theorems or principles yo have learned, NOT INTUITIONS. There are many seemingly reliable proofs which involves intuitions which proved later to be wrong.
Remember that in mathematics counterintuitive things happen. A lot.