In ABCD Quadrilateral, a parallogram?
(i)angle ABC is 90 DEGREE
(ii)angle ADC is 90 DEGREE


(a) (b) (c) (d)

• Both statements are necessary..
  Because for a quadrelatral to become a parllelogrm. one set of opposite angles should be equal (automatically 2nd set becomes equal if so)
  
  Here ABC = ADC = 90 which are opposite angles.
  More simplified it becomes a rectangle which is also a parllelogram
• 10 years agoHelpfull: Yes(19) No(12)
• no statement is sufficient because
  A |
  |
  |
  | D
  B |____/
  c
  In this case Both angles are 90
  but this is not a paralllelgram
• 10 years agoHelpfull: Yes(7) No(9)
• both statements are necessary
• 10 years agoHelpfull: Yes(5) No(5)
• none of the given statements are necessary...the quadrilateral has two opposite equal angles..that does not imply that it is a parallelogram...
• 9 years agoHelpfull: Yes(4) No(1)
• for Quadrilateral angle ABC + angle ADC =180
  (1)+(2) = 180
  therefore both equation help for quadrilateral
  option C
  
• 10 years agoHelpfull: Yes(3) No(5)
• Kindly note that, every sqauare and rectangle is one of the type of parallogram. More simplified
  
  Square (subset of) Rectangle (subset of) parallelogram (subset of) Quardrilateral. Most of them has mentioned in the solutions in the below manner
  
  1. If one pair of opposite angles are equal it's not a parallelogram.
  (No. This solution is wrong). If one pair of opposite angles of a quadrilateral are equal, then automatically the other pair of opposite angles will be equal.
  
  2. If the angle is 90deg then it is either a rectangle or square and not a parallelogram
  (By the defination of rectangle: A parallelogram whose opposite angles are 90deg is a rectangle and if the length of the adjacent sides are also equal then it's a square.
  
  So, from the question to prove that ABCD is a parallelogram both statements are necessary. And in this scenario the quadrilateral would either be a square or a rectangle which are one of the types of PARALLELOGRAM
• 8 years agoHelpfull: Yes(2) No(0)
• Both are insufficient .
  If both angles are 90 then it will be a square or a rectangle
• 10 years agoHelpfull: Yes(1) No(11)
• For parallelogram opposite angles should be equal , that is ok. but it should not be equal to 90 degree. Two opposite pairs are greater than 90 and other two opposite pairs are less than 90 degree. So answer should be none of above statements are sufficient
• 9 years agoHelpfull: Yes(1) No(0)
• either of statement is enough to say one angle is 90 all other are obv. 90 as the sum of adj. angle in a ||grm is 180 ; and all rectangles are parallelograms
• 9 years agoHelpfull: Yes(1) No(1)
• for a parallelogram if angle ABC is 90 Degree than it is compulsory that angle ADC to be 90 Degree.
  but if ABC is not 90 Degree then ADC will also not 90 Degree, In other words for an Parallelogram angle ABC should equal to angle ADC.
• 9 years agoHelpfull: Yes(1) No(0)
• both conditions should b there ..
  for any quadiletral to become a parallelogram atleast any two opposite angle should be equal ...
  if angle ABC = Angle ADC =90 then it become a rectangle or square that is also a parallogram ..
• 9 years agoHelpfull: Yes(0) No(0)
• necessary condition for parallelogram:
  1).both pair of opposite angles should be congruent .ie if ABCD is parallelogram then,
  
• 9 years agoHelpfull: Yes(0) No(0)
• ans- any single statement is necessary ... to find out that it is parallogram or not ... becouse parallogram does not have 90 angle
• 9 years agoHelpfull: Yes(0) No(0)
• A it is!!
  _| so |-
• 9 years agoHelpfull: Yes(0) No(0)
• Those who are saying that it is a rectangle not a parllelogram. Rectangle is also a parllelogram in which both opposite angles are 90 degree. Similarly rhombus and square are also a parallelogram.
• 9 years agoHelpfull: Yes(0) No(0)
• Including Both statement says that one pair of opposite set of angle in quadrilateral is equal and 90. But there is no way in which you can prove that quadrilateral is parallelogram.
• 9 years agoHelpfull: Yes(0) No(1)