Geometry Chapter 1 #12

[sunilpunjabi]

In the solution for #12 reads "Thus CE=2x=2(2)=4"
Then later in the same solution, when applying the Pythagorean Theorem the reads "6^2+b^2=10^2" to solve for b.
Why 6^2? If CE=4 then shouldn’t it read 4^2?

Is this s typo, or what am I missing?

[StaceyKoprince]

CE does equal 4 but the other leg of the triangle is not CE. The leg is EB, which is 6 - check out the diagram.

This illustrates the importance of drawing and completely labeling the picture. :)

[dl]

hi, i have a different question concerning this problem.

is there some type of theorem that states that line AE is the height of a trapezoid when a trapezoid is formed out of a rhombus or something to that effect? b/c unless it comes in a later chapter in the geometry guide how were we suppose to know that? i kinda err on the side of not always trusting the drawing and since there was no 90 degree symbol on line AD with the dotted line, i didnt want to assume anything.


thanks in advance!

[StaceyKoprince]

I think you meant line AE (the dotted line), not AD? In my book, that does indeed have a right angle symbol on it. Perhaps it was left out in a previous printing and has since been corrected. Yes, you'd need to have that info somehow.

[touchdownbuckeyes]

This is regarding problem #12 in the chapter 1 geometry set.

In calculating the area of trapezoid AECD, I do not understand how AE can be assumed as height of the trapezoid. Isn't AE one of the sides of the trapezoid? Is it considered as the height since
Angle AEC = 90?

Thanks.

[jnelson0612]

This is regarding problem #12 in the chapter 1 geometry set.

In calculating the area of trapezoid AECD, I do not understand how AE can be assumed as height of the trapezoid. Isn't AE one of the sides of the trapezoid? Is it considered as the height since
Angle AEC = 90?

Thanks.

Correct. Redraw the trapezoid so AD is the lower base of the trapezoid and EC is parallel to it on top. Notice how AE is the shortest distance between the bases? We know this is the case because it is a 90 degree angle. The shortest distance between the two bases is the height of the trapezoid.