Proofs In Plane Geometry

Properties Of Circles
1. tan. \perp rad.
2. rt. \angle in semicircle
3. \angles in same seg.
4. \angle at centre = 2 \angle at circ.
5. \angles in opp. seg. (a+c=b+d=180^\circ)
6. tan. from ext. pt.
Congruent & Similar Triangles

    \[\begin{array}{|c|c|} \hline \text{Congruent triangles} & \text{Similar triangles}\\\hline \text{SSS, SAS, AAS, RHS} & \text{SSS, SAS, AAA}\\\hline \end{array}\]

Midpoint Theorem
If D and E are the midpoints of AB and AC respectively, then DE // BC and DE=\dfrac{1}{2}BC.
Tangent-Chord Theorem (Alternate Segment Theorem)
If DE is a tangent to the circle at B, then \angle CAB=\angle CBE and \angle ACB=\angle ABD.