Question: Comparing Areas

Comment on Comparing Areas

considering the first given

considering the first given information that angle bce = 30 we can easily find out that this is a 30-60-90 triangle
Also as AC is the diagonal of rectangle ABCD therefore triangle ABC becomes 45-45-90 triangle which eventually fixes the way this fig looks so we can not extend or contract this figure to find out if this statement is sufficient or not.
However comparing these two triangles, we can easily find out bases of both triangle CBE and ABC, and from that information, we can find out base of triangle ACE and then we can compare bases of both triangles CBE ans ACE to answer our given question.So according to me this statement is sufficient.
Please correct me if I am wrong somewhere.

There's an error when you say

There's an error when you say: "Also as AC is the diagonal of rectangle ABCD therefore triangle ABC becomes 45-45-90"
IF we were told that ABCD is a SQUARE, then ABC definitely be a 45-45-90 triangle. However, we're told that ABCD is a RECTANGLE, in which case, we can't conclude that ABC is a 45-45-90 triangle.

Thanks for your quick response.Its clear now.

Brent,

Brent,

I did not understand why statement 1 is not sufficient.

The angle ACB is not 45°? so, ACE would be 15°?

Please explain me why am I wronging?

Thanks
Pedro

Hi Pedro,

Hi Pedro,

IF it were the case that ABCD is a SQUARE, then angle ACB would be 45°. However, we're not told that ABCD is a square.

Cheers,
Brent

Does this imply that

Does this imply that diagonals of rectangles are not angle bisector where as squares' are?

That is correct.

That is correct.

Here's an image that definitively shows that the diagonal of a rectangle is not an angle bisector: http://2.bp.blogspot.com/-TDhToIPWNFI/TkXXxns4JTI/AAAAAAAABB0/4accHIDqT1...

Cheers,
Brent