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Rhombus

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by prachich1987 » Sat Dec 18, 2010 12:16 am
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD


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Source: — Data Sufficiency |
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by Night reader » Sat Dec 18, 2010 12:53 am
prachich1987 wrote:Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD


Image

st(1) angle ADC=(360-2*angle BCD)/2=120, angle ADE=60 + angle BDA=60 (or angle ADE/2=60) => angle BDE=120 but angle BAE-? Not sufficient
st(2) AE // BD is the property for many quadrilaterals, Not sufficient for rhombus

Combining st(1&2) angles EAD=ADB, thus angle BAE=BDE=120. Satisfies for both properties of rhombus - // opposite sides and = opposite angles.

IOM C
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by prachich1987 » Sat Dec 18, 2010 1:03 am
Night reader wrote:
prachich1987 wrote:Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD


Image

st(1) angle ADC=(360-2*angle BCD)/2=120, angle ADE=60 + angle BDA=60 (or angle ADE/2=60) => angle BDE=120 but angle BAE-? Not sufficient
st(2) AE // BD is the property for many quadrilaterals, Not sufficient for rhombus

Combining st(1&2) angles EAD=ADB, thus angle BAE=BDE=120. Satisfies for both properties of rhombus - // opposite sides and = opposite angles.

IOM C
Here the positions of points B,D,A out of BDAE are fixed.
Now if we draw a line through point A parallel to BD ,it will meet the extended CD at point E.
So once we draw such parallel line ,the position of E is unique & we can do nothing about it.
So it has to be a rhombus.
Please tell me where I am going wrong
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by Rahul@gurome » Sat Dec 18, 2010 4:48 am
prachich1987 wrote:Here the positions of points B,D,A out of BDAE are fixed.
Now if we draw a line through point A parallel to BD ,it will meet the extended CD at point E.
So once we draw such parallel line ,the position of E is unique & we can do nothing about it.
So it has to be a rhombus.
Please tell me where I am going wrong
Your logic is good, but the conclusion is wrong.
For any rhombus ABCD, the point E is fixed. But that doesn't mean BDAE is rhombus too. Certainly BDAE will be a parallelogram but not always a rhombus. Statement 1 provides the crucial information that measure of angle BCD is 60 degrees which in turn implies the length of the diagonal of rhombus ABCD is also equals to the length of sides thus makes it a special rhombus. Only for that particular rhombus, BDAE is also a rhombus.
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by [email protected] » Sat May 26, 2012 1:48 am
I am getting the answer as C. Could somebody please help me in this question...

Statement 1 alone does not prove that AE is parallel to BD nor does it prove that Triangle AED is an equilateral triangle...


I need both the statements to prove that AEDB is also a Rhombus...

Help needed...
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by karthikpandian19 » Sat May 26, 2012 12:44 pm
Amit,

Refer here:
https://www.beatthegmat.com/mgmat-problem-t66431.html
[email protected] wrote:I am getting the answer as C. Could somebody please help me in this question...

Statement 1 alone does not prove that AE is parallel to BD nor does it prove that Triangle AED is an equilateral triangle...


I need both the statements to prove that AEDB is also a Rhombus...

Help needed...
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by patanjali.purpose » Sun May 27, 2012 1:31 am
[email protected] wrote:I am getting the answer as C. Could somebody please help me in this question...

Statement 1 alone does not prove that AE is parallel to BD nor does it prove that Triangle AED is an equilateral triangle...


I need both the statements to prove that AEDB is also a Rhombus...

Help needed...
We need both statements:

S1 gives us : <ADC = 120 ==> <ADB = 60 ==> <DAE+<DEA = 120

S2 tells us that AE is parallel with BD ==> angles <ADB = <DAE = 60 ==> <DEA = 60 ==> Traiangle ADE is equilateral ==> all sides of ABDE are equal.

IMO C
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by GMATGuruNY » Sun May 27, 2012 3:48 am
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD
Image
Statement 1: BCD = 60 degrees
In the figure below, ABDE is a rhombus:
Image
In the figure below, ABDE is not a rhombus:
Image
Insufficient.

Statement 2: AE||BD
In the figure below, ABDE is a rhombus:
Image
In the figure below, ABDE is not a rhombus:
Image
Insufficient.

Statements 1 and 2 together:
If BCD is 60 degrees, and AE||BD, then all of the angles shown must be 60 degrees, all the triangles shown must be equilateral, and ABDE must be a rhombus:
Image
Sufficient.

The correct answer is C.
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by amit28it » Mon May 28, 2012 3:58 am
I just want to give some general information about rhombus and I am giving the definition and properties of quadrilaterals as they are figures with four sides and four angles. There are many different types of quadrilaterals, which are classified by their sides and angles here are some examples-rectangle, parallelogram, trapezoid, rhombus, square and kite.
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