# 11X1 T13 04 converse theorems (2010)

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• Converse Theorems

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

90 semicircle ain

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

90 semicircle ain

(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.

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

90 semicircle ain

(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

P Q

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

90 semicircle ain

(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

P Q ABQP is a cyclic quadrilateral

• Converse Theorems (1) The circle whose diameter is the hypotenuse of a right angled

triangle passes through the third vertex.

A B

C ABC are concyclic with AB diameter

90 semicircle ain

(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

P Q ABQP is a cyclic quadrilateral

aresegment samein s

• (3) If a pair of opposite angles in a quadrilateral are supplementary (or

if an exterior angle equals the opposite interior angle) then the

• (3) If a pair of opposite angles in a quadrilateral are supplementary (or

if an exterior angle equals the opposite interior angle) then the

A

D

B

C

60

120

• (3) If a pair of opposite angles in a quadrilateral are supplementary (or

if an exterior angle equals the opposite interior angle) then the

A

D

B

C

60

120 ABCD are concyclic

• (3) If a pair of opposite angles in a quadrilateral are supplementary (or

if an exterior angle equals the opposite interior angle) then the

A

D

B

C

60

120 ABCD are concyclic

• (3) If a pair of opposite angles in a quadrilateral are supplementary (or

if an exterior angle equals the opposite interior angle) then the

A

D

B

C

60

120 ABCD are concyclic