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D is a point on side AC of ABC. Is ABC is isosceles? (1) The

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D is a point on side AC of ABC. Is ABC is isosceles? (1) The [#permalink] New post 03 Jul 2010, 15:44
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In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC
[Reveal] Spoiler: OA

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Re: Isosceles Triangle [#permalink] New post 03 Jul 2010, 20:29
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D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC

Can someone please explain the answer?

Sol:
1. Not sufficient.
D is a point on side AC of ΔABC. So there will be two triangles ΔABD & ΔDBC. Even if area is same this cant guarantee that Sides AB & BC are same. (sorry unable to draw picture here). Assume a case where AB=3,BC=2 and AD=4 & DC=6.

2. Sufficient.
It says BD┴AC & AD=DC.
Now imagine perpendicular BD as a wall in the middle of AC. since D is mid point (AD=AC)....any point on the wall will be equal distance from point A & C. So B is one of the point.

SO this goes as AB=CB i.e. AB=BC isosceles triangle.
Hence B.
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Re: Isosceles Triangle [#permalink] New post 01 Aug 2010, 07:56
ohfred wrote:
Hummm... I thought s1 also make sense.

IT doesn't because of the various variants of length with the same square.
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Re: Isosceles Triangle [#permalink] New post 30 Aug 2010, 19:02
devashish wrote:
D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC

Can someone please explain the answer?


Hi,
I think that the OA is wrong. It should be E.
Stmt 1: Insufficient. Equal areas of two sub-triangles formed does not gaurantee that it is an isoceles triangle.

Stmt 2: This statement means that BD is a perpendicular bisector of side AC. It divides AC in equal halves. i.e. the perpendicular bisector and Median co-incide. This doesnt prove that it is an Isoceles triangle as it can also be an Equilateral triangle.

Property of Equilateral and Isocele - The perpendicular bisector , the meadian and altitude drwan to a particular side all conicide i.e. all are same lines.

So we cannot conclude that it is an Isoceles triangle. It can also be an Equilateral triangle.

Ans -E
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Re: Isosceles Triangle [#permalink] New post 31 Aug 2010, 05:38
Expert's post
oldstudent wrote:
devashish wrote:
D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC

Can someone please explain the answer?


Hi,
I think that the OA is wrong. It should be E.
Stmt 1: Insufficient. Equal areas of two sub-triangles formed does not gaurantee that it is an isoceles triangle.

Stmt 2: This statement means that BD is a perpendicular bisector of side AC. It divides AC in equal halves. i.e. the perpendicular bisector and Median co-incide. This doesnt prove that it is an Isoceles triangle as it can also be an Equilateral triangle.

Property of Equilateral and Isocele - The perpendicular bisector , the meadian and altitude drwan to a particular side all conicide i.e. all are same lines.

So we cannot conclude that it is an Isoceles triangle. It can also be an Equilateral triangle.

Ans -E


An isosceles triangle is a triangle with at least two equal sides. So equilateral triangle is special type of isosceles triangle.

Answer B is correct.
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Re: Isosceles Triangle [#permalink] New post 31 Aug 2010, 06:09
Bunuel wrote:
oldstudent wrote:
devashish wrote:
D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC

Can someone please explain the answer?


Hi,
I think that the OA is wrong. It should be E.
Stmt 1: Insufficient. Equal areas of two sub-triangles formed does not gaurantee that it is an isoceles triangle.

Stmt 2: This statement means that BD is a perpendicular bisector of side AC. It divides AC in equal halves. i.e. the perpendicular bisector and Median co-incide. This doesnt prove that it is an Isoceles triangle as it can also be an Equilateral triangle.

Property of Equilateral and Isocele - The perpendicular bisector , the meadian and altitude drwan to a particular side all conicide i.e. all are same lines.

So we cannot conclude that it is an Isoceles triangle. It can also be an Equilateral triangle.

Ans -E


An isosceles triangle is a triangle with at least two equal sides. So equilateral triangle is special type of isosceles triangle.

Answer B is correct.


I agree with the same that in isoceles 2 sides are of same length. But after reading stmt 2 it is not clear whether its an isoceles triangle or equilateral triangle. Do you mean that even if it is an Equilateral traingle we can consider under Isoceles class? (as you said equilateral triangle is special type of isosceles triangle)

Please clarify. Thanks!
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Re: Isosceles Triangle [#permalink] New post 31 Aug 2010, 06:19
Expert's post
oldstudent wrote:
I agree with the same that in isoceles 2 sides are of same length. But after reading stmt 2 it is not clear whether its an isoceles triangle or equilateral triangle. Do you mean that even if it is an Equilateral traingle we can consider under Isoceles class? (as you said equilateral triangle is special type of isosceles triangle)

Please clarify. Thanks!


All equilateral triangles are isosceles triangles but not vise-versa.
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Re: D is a point on side AC of ABC. Is ABC is isosceles? (1) The [#permalink] New post 01 Feb 2014, 02:29
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Re: D is a point on side AC of ABC. Is ABC is isosceles? (1) The   [#permalink] 01 Feb 2014, 02:29
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