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# Is quadrilateral ABCD a parallelogram?

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Joined: 02 Sep 2009
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26 Sep 2016, 03:43
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Difficulty:

65% (hard)

Question Stats:

48% (01:04) correct 52% (01:01) wrong based on 153 sessions

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(1) All four internal angles of ABCD are equal.

(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

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Updated on: 26 Sep 2016, 12:23
Bunuel wrote:

(1) All four internal angles of ABCD are equal.

(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

from 1

for all regular polygons sum of angles included = (n-2)180 , in our case ....360 and since all angles inside are equal , then it is a regular quadrilateral with total angels divided equally ( given in 1) thus each angle measure is 90 , this is either a square or rectangle thus it is a parallelogram ....suff

from 2
2 adjacent triangles reflected through the diagonal will form a parallelogram or a kite ...insuff

Originally posted by yezz on 26 Sep 2016, 05:58.
Last edited by yezz on 26 Sep 2016, 12:23, edited 1 time in total.
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26 Sep 2016, 06:50
Bunuel wrote:

(1) All four internal angles of ABCD are equal.

(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

NOTE : A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some other
• A rectangle is a parallelogram but with all angles fixed at 90°
• A rhombus is a parallelogram but with all sides equal in length
• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

Stat 1: all internal four angles are equal...i.e. it can a square or rectangle...Sufficient.

Stat 2: Here it is given that both triangles are congruent but we don't have information whether two sides parallel are same or not...Insufficient.

IMO option A.
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26 Sep 2016, 10:37
3
yezz wrote:
Bunuel wrote:

(1) All four internal angles of ABCD are equal.

(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

from 1

for all regular polygons sum of angles included = (n-2)180 , in our case ....360 and since all angles inside are equal , then it is a regular quadrilateral with total angels divided equally ( given in 1) thus each angle measure is 90 , this is either a square or rectangle thus it is a parallelogram ....suff

from 2
2 adjacent triangles reflected through the diagonal will form a parallelogram ...suff

Conditions to be parallelogram:-
--->all angles equal or
---->2 opp.sides equal and parallel

(1) clearly suff....

(2) can be a square.....Yes
or
can be a Kite (SSS congruent)..fig. attached below.....No
insuff...

Ans A
Attachments

para.jpg [ 17.06 KiB | Viewed 6184 times ]

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26 Sep 2016, 12:21
rohit8865 wrote:
yezz wrote:
Bunuel wrote:

(1) All four internal angles of ABCD are equal.

(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

from 1

for all regular polygons sum of angles included = (n-2)180 , in our case ....360 and since all angles inside are equal , then it is a regular quadrilateral with total angels divided equally ( given in 1) thus each angle measure is 90 , this is either a square or rectangle thus it is a parallelogram ....suff

from 2
2 adjacent triangles reflected through the diagonal will form a parallelogram ...suff

Conditions to be parallelogram:-
--->all angles equal or
---->2 opp.sides equal and parallel

(1) clearly suff....

(2) can be a square.....Yes
or
can be a Kite (SSS congruent)..fig. attached below.....No
insuff...

Ans A

Brilliant many thanks
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Concentration: General Management, Strategy
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27 Sep 2016, 07:54
Definitely A

All angles can be equal for rectangle and square - which are special cases of parallelogram

Trapezoid and rhombus diagonals also divide the structure into equal parts. HEnce not sufficient
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29 Sep 2016, 22:52
1
1
A quadrilateral is parallelogram if ( min requirements and the more the better)

1- opposite sides are all parallel
2 opposite sides are congruent
3 a pair of opposite sides are congruent and parallel
4- 1 angle is supplementary to its 2 consecutive angles.
5 - every opposite pairs of angles are congruent
6- diagonals are congruent
7- diagonals ( both at the same time ) form 2 congruent triangles.

Rectangle is a parallelo + angles are all 90 ( but diagonals aren't perpendicular or don't bisect angles)
Square is a rectangle + diagonals are perpendicular bisector of each other or bisector of angles
Rhombus is parallelo with all sides congruent
Square is rhombus with angles 90 or with congruent diagonals that are perpendicular bisector of each other

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27 Jul 2019, 07:24
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