03
Sep
Question 8: If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Prerequisite
Primarily, this entire chapter is based on the cyclic quadrilateral and its properties. To prove that the given trapezium is cyclic, we need to prove that sum of its any pair of opposite angles is 180 degrees. We have used the following very important concepts of geometry in this proof.
- Same side interior angles formed on two parallel lines are supplementary
- Perpendicular distance between two parallel lines
- RHS congruence theorem
Theorem 6.4: If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
Theorem 7.5: (RHS congruence rule) : If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.
Chapter 10 – Circles
