Who Knows the Answer?

only add one straight line to make it is divided to two triangles.

No, you divided it to rectangle and trapezoid, I said add one straight line to divided to two triangles.

It's a block rectangle in 3d, the two scalene triangles fit together so....

The hypotenuse in the top picture is not straight. If you had not helpfully added the gridlines it wouldn't be as clear!

BTW I can't find an answer to Mandy's question.

neither one is straight, hold a straight edge up to the screen as I did......

The bottom one is straighter than the top. Where the amber part hits the hypotenuse you can see the difference in the gridlines.

It appears that they are equally off in opposite directions. Not unlike many people I work with.

You're right, they are off in opposite directions. The hypotenuse of the small dark green triangle has slope 2/5 = 0.4, for the whole figure it's 5/13, < 0.4. Not sure about equally, though.

Exactly right. In one case the smaller green triangle has an angle of 21.8 degrees and the larger red triangle has an angle of 20.6 degrees so the unit square is made up of the difference in the 'convex bowed hypotenuse' and the 'concave bowed hypotenuse'.

Yes, exactly equally off. (Same "hypotenuse", just flipped around.)

you said help me to improve my english, do you remember? See your mailbox.

This baffled the @#$% out of me so I laid it out in a CAD program. It turns out to be an optical illusion because when you stack these patterns in the two configurations, the hypotenuse is offset by approximately 1/5 of a square unit making up the area of the empty square.

Now I can proceed with my day.

Add a line; move a line.

Why not fold "it", making the appearance of one triangle, then add a single line to make two equal triangles? Or why not erase it and start over?

If that's the answer to this, the OP is going to take some heat for at least not mentioning a piece of paper. The only other method would involve mirror I'd say.

A line has no width one direction - maybe only a line segment but it only has length!

"Lines" in a road are about 4" wide. If a line had no width, how would you see it?

A line only has one direction? What are these?

The OP asked for a line, not a point.

These markers go from .25" to 1.5" wide, as with a pencil, if I draw across a piece of paper with any one of them, have I not made a line?

I see your point. Heehee. It's rectangular. :-))))

"...if I draw across a piece of paper with any one of them, have I not made a line?"

Only in the ordinary sense of the term, but not in the mathematical one, which is clearly the one required to solve the geometric puzzle presented. Surely, as (mostly) engineers and scientists, we can be a bit more precise? The "broad marker" concept works as a humorous answer, but not as a mathematical one. And, who knows? Perhaps the provided answer will also turn out to be just such a trick.

As for reply #14: those figures may represent curved line segments, but the puzzle asks for a "straight line" (and even if it hadn't been explicit, "straight" would have been implied by the term "triangle", a three-sided figure bounded by straight line segments - or by great circle segments, in the special case of a spherical triangle).

As to the actual solution: it seems impossible, given that:

1) Any line passing through two non-adjacent vertices leaves a triangle and a quadrilateral

2) Any line passing through a vertex plus one of the original boundaries will increase the number of defined segments

3) A line passing through TWO sides at locations other than vertices will, in general, add two more defined segments

4) Any line passing through two adjacent vertices leaves the problem unchanged (and whether two lines can occupy the same set of loci is usually stated by the author of any paper where the question arises, or set by the terminology used)

Yet, the very fact that the challenge was posed implies that there is some solution . . . Curiosity as to what it could be got me to subscribe.

May be your answer is right. Because there are many people's answer in china is same to you.

So do you know the answer?

You asked for the impossible, but 2 people did it.

Divided INTO two triangles? Equal triangles? Your problem needs clarification.

yeah,only add one straight line to divided it to two triangles, not equal triangles.

Give us the answer already!

She's struggling with the definition of line width.

I think Mandy has screwed up big time!........ She does not have a "proper" answer any more than we do!!!!

I am sure I remember from my school days that a "line" in such questions has length but no width effectively......please someone correct me if I am on the wrong "train"!....

Snel, I noticed that as well but discounted it as sloppy drawing.

I think you're on to the answer! I'll give ya a GA for that!

"Mandy said about a straight line which divides this shape into two triagles."

No, Mandy said "Add one straight line to make sure it is divided to two triangle." There is an apparent and obvious language disjoint, and at this time I still think that Snell is on track. This makes more sense than the 'fat line' solution.

You could do such a thing if the shape shown is, actually, a square folded on its corner... Then you unfold it and you do the job... ...

Considering a non flat (non Euklidean), 2 dimensional space, this is possible.

As an example, let's suppose that this shape is located on a cylindrical, 2 dimensional space. Then it is possible to draw a "straight line", dividing this shape into 2 triangles and 1 rectangular, as it is shown in this picture that I made.

The green line is considered as a "straight line" for someone who is located on this specific 2 dimensional space (cylinder). The same line is a spiral line (going around the cylinder all over again) for someone else who is located outside this cylinder. The orange areas show the two triangles.

That seems to be pushing things a bit!

"Divided" into two triangles implies the 2 triangles make up the original figure, and excludes triangles outside the original figure. If it had been "to produce 2 triangles" it would give more freedom in the answer.

Maybe it's a language issue.

Agree, it's a language issue. Mandy has already expressed her wish to improve her English (English Studying, posted in Education). I want to improve my English, too!What is meant in this case is probably "add straight line - produce 2 triangles". Mandy must have the last word.

brgds

Snel

Yes, Snel. If the original question was "add a straight line to produce two triangles" then this could be a solution.

Yes, I know that what I made doesn't provide an exact solution to the original question. This solution produces two triangles inside the original shape but doesn't divide the original shape into two triangles. At least, in this case I succeded to produce two triangles, without using "tricky" things, like "thick lines". Am I right?

I just wish She'd give the answer already. The post is already day's old and getting stale............

Maybe we have "outed" her and she is not going to come back.....

Just a thought!!!

I think it was a homework question.

It's obvious that she does not know the answer to the question she posed from her response earlier- "May be your answer is right. Because there are many people's answer in china is same to you."

That makes sense when looking over some of the posts from their profile as well.

I believe JPool nailed this one in post #9

Firstly, thanks everyone here to answer this questions, this question"only add one straight line to divide to this shape to two triangles", I do not know the answer, so I put it here, but I search the internet in china, the answer is like Jpool#9,Solar eagle#37,#38, thanks everyone.

It was childish and pointless, but what is new here on CR4 with some posters.....

I'm off, byeeeee