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• Feb 10th 2011, 06:18 PM
Quote:

Originally Posted by razemsoft21
Can you prove that:

AC is perpendicular to BD

This is the specific case when angles ADC and ABC are right angles.

Quote:

OR

AC divides BD into 2 equal parts
Again, those triangles would be right angled.

Quote:

OR

The angels ACB and ACD are equal ?
Those angles being equal can have the angles ADC and ABC both $>90^o$

in which case the quadrilateral would not be cyclic,
since opposite angles would not necessarily sum to $180^o$

Angles ADC and ABC either have to be right angled, or summing to $180^o$

Having them sum to $180^o$ is required.
• Feb 10th 2011, 07:22 PM
bjhopper
cyclic quardrilateral
Dear razemsoft,

If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees

bjh
• Feb 10th 2011, 08:09 PM
razemsoft21
Quote:

Originally Posted by bjhopper
Dear razemsoft,

If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees

Dear bjhopper
I know the properties of the kite very well, and as you know
the question is how to prove that the shape is a kite ?
• Feb 11th 2011, 02:53 AM
Quote:

Originally Posted by bjhopper
Dear razemsoft,

If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees

bjh

It has been shown that the quadrilateral can be cyclic even if those angles are not 90 degrees
even if someone refuses to see it.
• Feb 11th 2011, 07:10 AM
bjhopper
Proof of kite

Razemsoft's diagram

Connect DB
AC must be the perpendicular bisector of DB in order to produce the two equal x angles at A

AD=AB A is on the perp bisector
Triangles ADC and ABC are congruent SAS
Angle D = Angle B CPCT
Kite is defined

bjh
• Feb 11th 2011, 07:33 AM
Quote:

Originally Posted by bjhopper
Proof of kite

Razemsoft's diagram

Connect DB
AC must be the perpendicular bisector of DB in order to produce the two equal x angles at A

The above line is false

AD=AB A is on the perp bisector
Triangles ADC and ABC are congruent SAS
Angle D = Angle B CPCT
Kite is defined

bjh