Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Sep 2013
Posts: 220
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Rhombus [#permalink]
Show Tags
15 Dec 2013, 16:42
Bunuel wrote: 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 AEBD and BADE), 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



Math Expert
Joined: 02 Sep 2009
Posts: 39698

Re: Rhombus [#permalink]
Show Tags
16 Dec 2013, 01:06
AccipiterQ wrote: Bunuel wrote: 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 AEBD and BADE), 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Sep 2013
Posts: 220
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Rhombus [#permalink]
Show Tags
16 Dec 2013, 12:14
Bunuel wrote: AccipiterQ wrote: Bunuel wrote: 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 AEBD and BADE), 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



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: Rhombus [#permalink]
Show Tags
11 May 2014, 13:33
Bunuel wrote: 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 AEBD and BADE), 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.



Math Expert
Joined: 02 Sep 2009
Posts: 39698

Re: Rhombus [#permalink]
Show Tags
12 May 2014, 02:11
russ9 wrote: Bunuel wrote: 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 AEBD and BADE), 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 foursided shape is a quadrilateral. 3 is correct.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: Rhombus [#permalink]
Show Tags
15 May 2014, 17:20
1
This post was BOOKMARKED
Bunuel wrote: russ9 wrote: Bunuel wrote: 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 AEBD and BADE), 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 foursided shape is a quadrilateral. 3 is correct. Thanks a ton. Very clear now.



Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
14 Jul 2015, 07:35
AccipiterQ wrote: Bunuel wrote: 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 AEBD and BADE), 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 Important thing to remember here: Rhombus is a symmetrical quadrilateral wrt the diagonals. What this means is that any diagonal will divide the rhombus into 2 triangles of equal areas. Also, because of the symmetry it is easy to prove that \(\angle A = \angle C\). Additional properties of rhombus are: •Opposite angles of a rhombus have equal measure. •The two diagonals of a rhombus are perpendicular •Its diagonals bisect opposite angles. Draw BD to complete triangle ABD. Given, \(\angle {BCD}\) = 60 degrees. > \(\angle {BAD}\) = 60 degrees and \(\angle {ABC}\) = \(\angle {CDA}\) = 120 degrees (to complete 360 degree for sum of all internal angles of a quadrilateral). Now, diagonal BD will bisect \(\angle {CBA}\) and \(\angle {CDA}\) such that \(\angle {ABD} = \angle {ADB}\) = x. Thus, in triangle ABD, x+x+60 = 180 > x = 60 degrees . Thus triangle ABD is equilateral and hence AB = BD.
_________________
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidatedthursdaywithronlistforallthesections201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmatmathbookindownloadablepdfformat130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalitiesmadeeasy206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalitiestipsandhints175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650to750a10monthjourneytothescore203190.html



Manager
Joined: 10 Mar 2014
Posts: 245

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
05 Aug 2015, 06:49
Bunuel wrote: russ9 wrote: Bunuel wrote: 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 AEBD and BADE), 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 foursided shape is a quadrilateral. 3 is correct. hi bunuel, could you please clarify ABDE is a parallelogram (as AEBD and BADE). I just want to know on what basis we are saying ABDE is parallelogram. I am not clear about this. Thanks



Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
05 Aug 2015, 07:02
PathFinder007 wrote: hi bunuel,
could you please clarify ABDE is a parallelogram (as AEBD and BADE). I just want to know on what basis we are saying ABDE is parallelogram. I am not clear about this.
Thanks Any quadrilateral with 2 pairs of parallel lines is a parallelogram. All shapes such as rectangles, rhombuses, squares are parallelograms
_________________
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidatedthursdaywithronlistforallthesections201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmatmathbookindownloadablepdfformat130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalitiesmadeeasy206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalitiestipsandhints175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650to750a10monthjourneytothescore203190.html



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15982

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
28 Nov 2016, 06:00
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Joined: 12 Nov 2016
Posts: 365

Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
19 Apr 2017, 17:01
http://www.mathprof.com/Geom/Ch_22_Fig_02.jpg I think this picture helps it clearly explains the structure of a rhombus imo not all diagrams are created equal (e.x many transversals diagrams show a line decreasing from left to right that intersect two parallel lines but a transversal can also be a right increasing from left to right that cuts through two parallel lines for some people being shown both diagrams can really help them with spatial awareness). Also, a rhombus is basically an equilateral parallelogram I find this gives me a much clearer understanding of the relationships between the two figures. From statement 2 we could still have a figure that is a parallelogram, or in other words, only two sides are equal instead of all four. Statement 2 is basically a trap answer/ categorization fallacy the test makers know people are likely to pick.



Senior Manager
Joined: 09 Feb 2015
Posts: 334
Location: India
Concentration: Social Entrepreneurship, General Management
GPA: 2.8

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
19 Apr 2017, 23:34
Bunuel wrote: 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 AEBD and BADE), 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. Since we know all angles in triangle ADE is 60 and since one of the sides is AD ,can we not infer that all sides of triangle ADE are equal and hence All sides of Rhombus ABDE are equal.? What am i missing here?



Math Expert
Joined: 02 Sep 2009
Posts: 39698

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Show Tags
19 Apr 2017, 23:43
goforgmat wrote: Bunuel wrote: 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 AEBD and BADE), 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. Since we know all angles in triangle ADE is 60 and since one of the sides is AD ,can we not infer that all sides of triangle ADE are equal and hence All sides of Rhombus ABDE are equal.? What am i missing here? Are you talking about the first statement? If yes, then from (1) we k ow that BCD and ABD are equilateral, not ADE.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: Quadrilateral ABCD is a rhombus and points C, D, and E are
[#permalink]
19 Apr 2017, 23:43



Go to page
Previous
1 2
[ 33 posts ]




