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# Geometry Problem URGENTTTTTT

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Joined: 06 Oct 2011
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10 Nov 2011, 08:54
Q1 .In this diagram, AB=AC. and BD=CD. Which of the following statements is true?
A. BE=EC
B. AD is perpendicular to BC
C. triangle BDE and CDE are congruent
D. angle ABD equal angle ACD
E. All of these

Figure: SEE ATTACHMENT

Please give explanation for each of these why something is not true

Q2. ABCD is a rectangle; the diagonals AC and BD intersect at E. Which of the following statements is not necessarily true?

A. AE=BE
B. Angle AEB equals angle CED
C. AE is perpendicular to BD
D. Triangles AED and AEB are equal in area
E. Angle BAC equals angle BDC

Pls give full explanation
Attachments

File comment: ATTACHMENT FOR QUESTION 1

ar.JPG [ 14.25 KiB | Viewed 1169 times ]

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11 Nov 2011, 17:02
E / C

Q1.

AB=AC, BD=CD
-> ABC, DBC are isosceles triangles respectively.
-> Angle ABD = Angle ACD
-> Triangle ABD = Triangle ACD
-> BC is perpendicular to AD (because Triangle ABC is isosceles.)

-> Triangel ABE=ACE, DBE=BCE,
and Angle AEB=AEC=DEB=DEC=90
A. BE=EC <- true, Triangel AEB=AEC
B. AD is perpendicular to BC <- true
C. Triangel BDE=CDE <- true
D. Angle ABD=ACD <- true
E. all true <- true

Q2.

and, according to the symmetricalness of rect., AE=BE=CE=DE
-> tri. AEB=CED : isosceles,
tri. BEC=AED : isosceles.

A. AE=BE <- true
B. ang. AEB=CED <- true; vertical angles.
C. AE perpend. BD <- not necessarilly; true only when the rect. is a square.
D. tri. AED and AEB are equal in area <- true; these 2 triangles are 2 parts of tri. ABD. When you assume BE and DE are the bases of each tri., they are sharing the height. So, they have the same height and the same length of the base, and thus the same area.
E. ang. BAC=BDC <- true; tri. EAB=EDC.

Re: Geometry Problem URGENTTTTTT   [#permalink] 11 Nov 2011, 17:02
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