Summary Paper 2 theorem proofs grade 12 IEB

This document includes how to solve grade 12 proofs. The line segment joining the centre of the circle and the midpoint of a chord is perpendicular to the chord. An angle at the centre of a circle equals twice an angle at the circumference subtended by the same arc. The opposite angles of a cyclic quadrilateral are supplementary. The angle between a tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment. Ratio of areas equals ratio of bases. Ratio of areas equals ratio of corresponding sides squared. A line drawn parallel to one side of a triangle divides the other two sides proportionally. If two triangles are equiangular, then their corresponding sides are in the same proportion and hence the triangles are similar. A line drawn from the vertex at the right angle of a right angled triangle, perpendicular to the hypotenuse, divides the triangle into two triangles which are similar to each other and the original triangle. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides