HELP ME with GEOMETRY

[arifaisal]

In the diagram above, AB=CD, From this we can deduce that: A) AB is parallel to CD. B) AB is perpendicular to?
In the diagram above, AB=CD, From this we can deduce that:
A) AB is parallel to CD.
B) AB is perpendicular to BD.
C) AC=BD
D) Angle ABD equals angle BDC.
E) Triangle ABD is congruent to triangle ACD

Picture reference: https://www.pagalguy.com/forums/gmat-and ... /r-2577147

Please explain in details and simple words, im not getting it from the other site.

[limestone]

Hi there,

Sorry I cannot post the picture (Error 404). Please find the attachment here as reference (I draw an addition red line to the original diagram).

The answer should be D or angle ABD equals to angle BDC.

The reason is:

Angle ABD = angle ABC + angle CBD
Angle BDC = angle BDA + angle ADC

angle ABC = angle BAC (angles substended on the same arc - Circle Theorems) (I)
angle CBD = angle ADC (Arc AB = Arc CD, both of the angle are acute) (II)
(Please note the when arc AB overlap arc CD, AB=CD, then angle CBD is not equal to angle ADC but their sum is 180 degree instead. The equality happens only when the 2 angles are both acute or obtuse. Please check theorems of angle in circles should anything be unclear)
From (I) and (II), angle ABD = angle BDC.

Elimination:
B,C,E happen only when A happen. The original diagram make AB and CD seem to be paralleled, but they do not necessary to be so. I also attach a rebuilt version here for your reference.


Hope it helps.