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Quadrilateral ABCD is a rhombus and points C, D, and E are

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Re: Rhombus [#permalink] New post 16 Dec 2013, 00:06
Expert's post
AccipiterQ wrote:
Bunuel wrote:
Image
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


How do you know that BD=AB from 1?? Is there some hidden calculations done in there? All I see is BCD=60, you don't know the measures of any other angles so it doesn't really tell you anything


Because BC=CD, triangle BCD is isosceles. (1) says that angle BCD is 60 degrees, thus triangle BCD is equilateral. Therefore BD=BC=CD.

Hope it's clear.
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Re: Rhombus [#permalink] New post 16 Dec 2013, 11:14
Bunuel wrote:
AccipiterQ wrote:
Bunuel wrote:
Image
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


How do you know that BD=AB from 1?? Is there some hidden calculations done in there? All I see is BCD=60, you don't know the measures of any other angles so it doesn't really tell you anything


Because BC=CD, triangle BCD is isosceles. (1) says that angle BCD is 60 degrees, thus triangle BCD is equilateral. Therefore BD=BC=CD.

Hope it's clear.



Perfectly, I should have read the question more thoroughly. Thanks
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Re: Rhombus [#permalink] New post 11 May 2014, 12:33
Bunuel wrote:
Image
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.
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Re: Rhombus [#permalink] New post 12 May 2014, 01:11
Expert's post
russ9 wrote:
Bunuel wrote:
Image
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

1. From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

2, Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

3. Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.


1 is correct.
2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral.
3 is correct.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Rhombus [#permalink] New post 15 May 2014, 16:20
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Bunuel wrote:
russ9 wrote:
Bunuel wrote:
Image
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

1. From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

2, Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

3. Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.


1 is correct.
2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral.
3 is correct.


Thanks a ton. Very clear now.
Re: Rhombus   [#permalink] 15 May 2014, 16:20
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