<p>I stumbled upon this question in the 8 Real SATs I managed to find in a bargain store. I think it's pretty easy for many, but so far I couldn't grasp the whole point of the item. If it's my carelessness or my sheer ignorance, I don't know. Here goes:
..... A
....../l\
...../ l \
.../ . l . \
B/_ xly_.\C
D
Figure not drawn to scale
(x and Y are supplementary angles, <BDA and <CDA respectively)</p>
<p>Question:
In Triangle ABC above, AD=AC. Which of the following must be true?</p>
<p>(A) AB=BC
(B) x=y=90
(C) Area of Triangle ABD = Area of triangle CBD
(D) Perimeter of ABD = perimeter of CBD
(E) Measure of <BAD = measure of <BCD
(Please ignore the dots and my futile attempt to a decent triangle)</p>
<p>The answer is C, and I can't fully get why this is so. Please enlighten me. Thank you.</p>
<p>uhh... What is D??
I mean its a triangle ABC with 3 points. Whats D?
Clarify and U'll get a reply :D</p>
<p>Ah, yeah, thank you for pointing that out.</p>
<p>D is the midpoint of BC. :)</p>
<p>Here's the edited triangle:</p>
<p>..... A
....../l\
...../ l \
.../ . l . \
B/_ xly_.\C
......D</p>
<p>Area of triangle CBD doesn't exist, it's a straight line.</p>
<p>well isn't it C because the height and base for each would be be same?</p>
<p>ecnerwalc3321 is right...it has no area..it's one dimensional...there's an error in the writeup somewhere.</p>
<p>Here's the more precise triangle:</p>
<p><a href="http://suigeneris.snoozland.com/question.jpg%5B/url%5D">http://suigeneris.snoozland.com/question.jpg</a></p>
<p>In Triangle ABC above, AD=AC. Which of the following must be true?</p>
<p>(A) AB=BC
(B) x=y=90
(C) Area of Triangle ABD = Area of triangle CBD
(D) Perimeter of triangle ABD = perimeter of triangle CBD
(E) Measure of <BAD = measure of <BCD</p>
<p>Thanks :)</p>
<p>How the f*** does AD=AC? That isnt possible. Check what it says in the book.</p>
<p>Thats impossible for AD to equal AC. Unless its a three dimensional triangle.</p>
<p>If it is a three dimensional triangle with point D sticking out from the paper towards you, then it must be assumed for x and y to be supplementary (meaning that x+y=180) that x=y=90.</p>
<p>You should draw the bottom of the triangle on a paper, and point ur pencil from the point D straight up to mimic a three dimensional triangle. Then you will see why the three dimensional model is x=y=90.</p>
<p>yea.. paradox is right... if they are equal a^2+b^2 doesn't equal c^2 cause the other leg can't be 0. :(</p>
<p>Harping, it is most likely wrong. Unless it is a three dimensional triangle. With point D sticking out at you from the paper. Try imagining it, its quite a mind bending excersise.</p>
<p>Are you sure the question says AD = AC and not AD = DC?</p>
<p>If AD = DC, then both triangles have the same height BD and the base would be the same and you just do A = 1/2bh, so both triangles have same area.</p>
<p>You made a typo somewhere.</p>
<p>OMG. I'm sorry again. It's BD=CD.</p>
<p>Ah. The stress of the possibility of not being able to take the SAT this December is getting on me... :(</p>
<p>I think ur playing a joke on us, which is not very nice, cus if BD = CD and D is the midpoint of AC then all of the above is true.</p>
<p>I'm sorry. I'm not playing a joke I swear. This is the last time, and I'm sure about this:</p>
<p>AD=DC</p>
<p>A. AB = BC. Not necessarily. From the given information, we can't confirm if BD is actually perpendicular to AC.
B. x = y = 90. Again, we can't tell for sure for the same reason as above.
C. Area of ABD = Area of CBD. Is the answer according to the book. Triangles ABD and CBD have the exact same height and base (since AD = DC), thus the same areas.
D. Perimeter of ABD = Perimeter of BCD. It will only be true if BD is perpendicular to AC, which, as above, we can't tell for sure.
E. <BAD = <BCD. Is not the answer for the same reason above. </p>
<p>LOL, the first time I read the question (the one on the first post of this thread), I thought I was seeing something.</p>
