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In the figure above, is XW = XZ? (1) The area of triangular region ZX

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In the figure above, is XW = XZ? (1) The area of triangular region ZX  [#permalink]

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New post 17 Sep 2018, 21:18
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Question Stats:

38% (01:51) correct 62% (01:49) wrong based on 63 sessions

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In the figure above, is XW = XZ?

(1) The area of triangular region ZXY is equal to the area of triangular region WXZ.
(2) Angle XZW is equal in measure to angle XZY.


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Re: In the figure above, is XW = XZ? (1) The area of triangular region ZX  [#permalink]

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New post 17 Sep 2018, 21:37
In the figure above, is XW = XZ?

(1) The area of triangular region ZXY is equal to the area of triangular region WXZ.
(2) Angle XZW is equal in measure to angle XZY.

From stmnt 1: we can say that zy equals wz since area of triangle 1/2 * base * height so both values of base must be equal to get same area.

from stmnt 2: angle xzw = angle xzy means it is perpendicular bisector and each angle measures 45 *.

Combining both stmnts we can deduce that wz=zy and xz is common so sides xw=xy.

IMO C should be right..
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Re: In the figure above, is XW = XZ? (1) The area of triangular region ZX  [#permalink]

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New post 17 Sep 2018, 22:00
archish3113 wrote:
In the figure above, is XW = XZ?

(1) The area of triangular region ZXY is equal to the area of triangular region WXZ.
(2) Angle XZW is equal in measure to angle XZY.

From stmnt 1: we can say that zy equals wz since area of triangle 1/2 * base * height so both values of base must be equal to get same area.

from stmnt 2: angle xzw = angle xzy means it is perpendicular bisector and each angle measures 45 *.

Combining both stmnts we can deduce that wz=zy and xz is common so sides xw=xy.

IMO C should be right..


Hi archish3113,

Can you explain a bit more as to how each angle measure is 45* as you mentioned in "angle xzw = angle xzy means it is perpendicular bisector and each angle measures 45 *".

Also, when you say "we can deduce that wz=zy and xz is common so sides xw=xy", you are proving that xw=xy, however question is asking whether XW = XZ.
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Re: In the figure above, is XW = XZ? (1) The area of triangular region ZX  [#permalink]

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New post 01 Dec 2018, 03:24
Statement 1 = give us The area of triangular region ZXY is equal to the area of triangular region WXZ.
= they both have same height
=> wz = zy
No information about XW and XZ. hence not Sufficient

Statement 2 = Angle XZW is equal in measure to angle XZY.
means it is perpendicular bisector and both angle must be equal to 90.

For XW = XZ angle XWZ must be equal to 90. using the property isosceles triangle "If in a triangle two angles equal one another, then the sides opposite to the equal angles also equal one another."

This is a impossible case , hence XW will never going to be equal to XZ.

Statement 2 is sufficient

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