Question

In this figure, line AB and CD are parallel.

AB is perpendicuar to line segment [CF/FH/DH/GH]

If the length of EF is a units, then the length of GH is

[a/b/a+b/a-b]

Answer 1

https://cdn.ple.platoweb.com/EdAssets/39ab3bb25f694379bc26ca0358256c80?ts=635366577230970000

Answer 2

@mathmate

Answer 3

There are many ways to approach this problem.
One of them is to show that quadrilateral EFHG is a rectangle, and then use the properties of a rectangle.
Another way is to prove that triangles EFG and HGF are congruent.
Depending on your previous knowledge of geometry, you can choose between the two, or, even better, propose your own method.

Answer 4

@mathmate So could you explain in more detail please?

Answer 5

If you choose one of the above methods that require proofs that you are familiar with, I will be glad to work with you. If you have another idea, bring it forward, and we can work with it. I am not planning to go in detail in monologue though.

Answer 6

Im not good with this stuff so I'll choose method A :o

Answer 7

@mathmate

Answer 8

As far as you know, what is the definition of a rectangle. In other words, under what conditions will a quadrilateral be considered a rectangle?

Answer 9

a square except 2 sides are longer?

Answer 10

You are using a recursive definition, i.e. using another math term to define a rectangle. The question would be what makes a square.
The following link might help you.
http://www.mathopenref.com/rectangle.html

Answer 11

Oh well.... :L

Answer 12

By the way, a square IS a rectangle, because both a square and a rectangle fits the definition of a rectangle.

Answer 13

*fit

Answer 14

why is math so complicated
I get taught that a square is a box with all equal sides and 4 sides, and that a rectangle is the same but 2 sides are longer.

Answer 15

now im bein told they're the same thing

Answer 16

;-;

Answer 17

Your definition is a layman's definition, not math. If you're doing geometry, read the link I gave you.

Answer 18

I did :P

Answer 19

Your teacher describes what a rectangle looks like to help you understand, he/she was not giving you the definition of a rectangle.

Answer 20

So what makes a rectangle?

Answer 21

"A 4-sided polygon where all interior angles are 90°"

Answer 22

Excellent. So to find GH, we need to show that EFHG is a rectangle.
By the way, the information given in the question is incorrect:
`AB is perpendicuar to line segment [CF/FH/DH/GH]`
should read parallel instead of perpendicular.
You may want to check your source.

Answer 23

What do you know about consecutive interior angles?

Answer 24

Uh
Nothing?

Answer 25

are those the 2 lines that are parallel and then there is a diagonal line going through them

Answer 26

that

Answer 27

Excellent.

By virtue of the fact that consecutive interior angles are supplementary, what's the unknown angle?