2. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex.
3. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. A B C
4. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter A B C
5. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter A B C
6. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter (2) If an interval AB subtends the same angle at two points P and Q on the same side of AB, then A,B,P,Q are concyclic. A B C
7. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter (2) If an interval AB subtends the same angle at two points P and Q on the same side of AB, then A,B,P,Q are concyclic. A B C A B P Q
8. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter (2) If an interval AB subtends the same angle at two points P and Q on the same side of AB, then A,B,P,Q are concyclic. ABQP is a cyclic quadrilateral A B C A B P Q
9. Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled triangle passes through the third vertex. ABC are concyclic with AB diameter (2) If an interval AB subtends the same angle at two points P and Q on the same side of AB, then A,B,P,Q are concyclic. ABQP is a cyclic quadrilateral A B C A B P Q
10. (3) If a pair of opposite angles in a quadrilateral are supplementary (or if an exterior angle equals the opposite interior angle) then the quadrilateral is cyclic.
11. (3) If a pair of opposite angles in a quadrilateral are supplementary (or if an exterior angle equals the opposite interior angle) then the quadrilateral is cyclic. A D B C
12. (3) If a pair of opposite angles in a quadrilateral are supplementary (or if an exterior angle equals the opposite interior angle) then the quadrilateral is cyclic. ABCD are concyclic A D B C
13. (3) If a pair of opposite angles in a quadrilateral are supplementary (or if an exterior angle equals the opposite interior angle) then the quadrilateral is cyclic. ABCD are concyclic A D B C
14. (3) If a pair of opposite angles in a quadrilateral are supplementary (or if an exterior angle equals the opposite interior angle) then the quadrilateral is cyclic. ABCD are concyclic Exercise 9D; 1, 2, 3, 6b, 7b, 10a, 11 A D B C
