# Proofs In Plane Geometry

Properties Of Circles
1. tan. $\perp$ rad.
2. rt. $\angle$ in semicircle
3. $\angle$s in same seg.
4. $\angle$ at centre = 2 $\angle$ at circ.
5. $\angle$s 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 $\angle ACB=\angle ABD$.
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