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Geometry:Right angle property

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Source: — Data Sufficiency |
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by rijul007 » Mon Dec 12, 2011 8:17 am
Statement 1
AC perpendicular to BD
tells us nothing

Its insufficient


Statement 2
BC = CD

We have no clue what point C is..
Insufficient


Combining two statements ...
AC perpendicual to BD and BC= CD

triangle ACB and triangle ACD will be congruent
AB = AC = 5
BC = 5*rt(2)


Option C
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by Anurag@Gurome » Mon Dec 12, 2011 9:48 pm
zaarathelab wrote:Pls see attachment.
If Triangle BAD is a right angle, what is the length of side BD?

1)AC is perpendicular to BD
2)BC = CD

Experts, need your comments
(1) AC is perpendicular to BD does not help us to find the length of BD; NOT sufficient.

(2) BC = CD
Triangles ACB and ACD are congruent to each other, as BC = CD, AC = AC(common). Since the two triangles are congruent, so AB = AD = 5. BAD is right angled at A, so by Pythagoras Theorem, we can find BD; SUFFICIENT.

The correct answer is B.
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by zaarathelab » Tue Dec 13, 2011 12:43 am
OA is C

Anurag, can you pls illustrate the relationships in this special type of right angled triangle with respect to:
1. AC is perpendicular to BD
2. AC is a median
3. AC is a perpendicular bisector of BD

My take

1. AC is perpendicular to BD MEANS AC^2 = BC*CD (All triangles are similar)
2. AC is a median MEANS BC=CD and all triangles are similar (BA=BC) ABD is an isoceles triangle (AD=AB)
3. AC is the perpendicular bisector of BD MEANS BC=CD and all triangles are similar (BA=BC) ABD is an isoceles triangle (AD=AB)

I often get confused with this type of triangle

Thanks
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