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Math Forum - Problem of the Week
Submissions for Triple Tango
135 threads found, displaying 1 to 50.[First/Prev] 1, 2, 3 [Next/Last]
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Short Answer
Long Answer
Submitters School
11/25/2002
The following trieangles go
together triangle 4 and
triangle 2, triangles 3 and 6,
and triangles 1 and 5.
What I did was I would look for common lengths in the triangles, and
if i found one i would add the angles near together, and if one of
the angles equalled 180 degrees they were the right matches. I
continued this process until i found three pairs.
79260
[n/a]
11/25/2002
Triangles 1 & 5 are a pair,
triangles 6 & 3 are a pair, &
triangles 2 & 4 are a pair.
Triangles 1 & 5 are a pair, triangles 6 & 3 are a pair, & triangles
2 & 4 are a pair. First, I matched up the sides of the triangles
with equal sides. Then, those sides on one angle must make a 180
degree angle, a strait line. Then, to check my work, I added
together all of the sides of the triangle and checked that they
equaled 180 degrees.
79033
[n/a]
11/25/2002
Triangle 1 goes with triangle To solve this problem, I just needed to know some basic geometry
rules. One, is that a triangle has angles that equal 180 degrees.
5. Triangle 4 goes with
Two, that you need congruent sides in order to not overlap.
triangle 2. Triangle 3 goes
with triangle 6. First, you
want congruent sides from
two triangles. For example:
Triangle 1 has a side with a
measure of 4.5 and so does
triangle 5. Next, you have t
78340
2010
11/25/2002
Triangle 1 and 5, 2 and 4, 9 I cut the papers out, and then matched the sides!
and 3 each pair up to form
a bigger triangle
79335
8713
11/25/2002
You can put triangle 1 and 5 Well the process I used to solve this problem was that I looked for
congruent sides on which you could combine 2 triangles without
together at sides LG and
letting them overlap.
AB; you can put together
triangles 3 and 6 at side HG
and side XY; and you can
put together triangle 2 and
4 by sides MO and RQ.
79395
[n/a]
11/25/2002
This page is very nice.
i cut up the pieces and arranged do that they looked like they fit
together good.
79397
793
11/25/2002
The three triangles i formed
were by combining triangle
one and triangle 5, triangle
2 and 4, and triangle 6 and
3.
In order to find out which triangles go together, i considered what
you need to make a triangle; 3 sides and interior angles that add up
to 180 degrees. It took me a while to find out which triangles would
go together, but i started out finding two sides that were of equal
length, and randomly put them together and added up all three of the
new corners to see if they add up to 180. Since triangle one's 4.5
side was the only side that matched with another measure on only
trianle 5, i tried those first and they worked, when i put line seg
LJ against line seg BC, then added up the angles in triangle A(CL)K
it added up to 180 degrees. I did this using the side on triangle 6
of 3.4 to find that when matching line seg XY with HG, triangle ZP
(GY)'s angles added up to 180 degrees. THat left me with triangles 2
and 4. I took the angles from triangle 4 and subracted each from 180
to see if the answer matched any of the angles on triangle 2. Since
to make two of the angles connect to form a straight line they must
add up to 180. I found that angle M plus angle Q equaled 180
degrees. So i added up the rest of the angles to find out tha when
you make triagle NRO All the angles add up to 180.
78268
3004
A general descrition for the connection of triangle STU and DEF is
two of the angles must be put together to equal a straight line of
180 degrees, then, the newly formed triangle must have only 3 sides
and 3 angles...the angles must add up to 180 degrees by def. of the
sum of the agles of a triangle.
1 of 6
11/26/2002
(1,5)/ (3,6)/ (2,4)
The sides of the triangles that are going to be put together have to
be congruent and one if the angles of the triangle has to add up to
180 degress when they are added to make a straight line (180
degrees), so that the angles of the triangle all together will equal
180 and be a true triangle.
79089
[n/a]
11/26/2002
The answer to "Triple
Tango" is the following.
Triangle #1 with #5, triangle
#3 with #6 and triangle #2
with #4.
To figure out which two triangles make a larger triangle, you measure
the degrees of the triangle. The total of the three angles for the
larger triangle must equal to 180 degrees. Also, any two adjacent
triangles making up a straight line must equal to 180 degrees. For
example, when #1 and #5 are joined at the 4.5" side,
79050
17298
11/24/10 1:22 PM
The Math Forum @ Drexel University
Created
11/26/2002
Thread
History
http://mathforum.org/pows/print/submissions.htm?publication=...
Short Answer
Triangle ABC and triangle
JKL by AB to LJ, triangle
PQR to triangle OMN by
OM to RQ, triangle XYZ and
triangle HGI by WY to HG.
Long Answer
A line that divides a triangle into two triangles will create a pair
of supplementary angles.
Using this logic, I found pairs of supplementary angles and adjacent
corresponding congruent sides since (the line divison between two
triangles to create a larger triangle).
Submitters School
78872
1448
79405
[n/a]
Triangles DEF and STU will have a pair of supplementary angles and at
least one adjacent congruent side in order to form a larger triangle
when put together.
11/26/2002
piss balls ass toldo totti shit
1. christmas porn dick-o
clown we all make very
good porn and a dick came
to jimmy's ass and laid
some creepy faget shit
hawk porn 2. Bite my shit
kill my clit and call me a ball
tongue 3. eat my ass
11/26/2002
i think 3 and 4 look good
together
who cares they fit real nice
79406
[n/a]
11/26/2002
The final answer is 5.
I used guess and check.
79407
[n/a]
11/26/2002
The three pairs of triangle
that can be put together to
form another, larger tringle
are triangles 1 and 5,
triangles 2 and 4, and
triangles 3 and 6.
The two triangles you are trying to combine to form a larger one must
have lines with equal lengths that combine to become a shared side.
Also, one angle from both of the triangles must be able to combine
with the other to make a linear pair, two angles that form a straight
line(180 degrees), so that they can form a straight line. This
prevents another vertex from producing, making the figure into a
quadrilateral.
To find the answer to the problem, I found all the possible pairs of
triangles that can form another, and picked out three that had no
numbers twice in all of them.
79066
[n/a]
11/26/2002
Triangles 1 and 5, 6 and 3,
and 2 and 4 are the pairs of
triangles. You would look
for two angles that equal
180 degrees and then see if
the sides that make up the
angle match upor are equal
to each other.
First thing that I did was found triangles that had sides that
matched up. Then I looked at the angles in the triangles and added
them to other angles to get 180 degrees. Then by trial and error I
matched the triangles together.
77917
15764
11/26/2002
jojojojojojo
lasdkjlas-20395-23094as;dlkma;sldf,
79067
[n/a]
11/26/2002
I think the answer is 30
degrees.
This is what i got when i added them up.
78602
3508
11/26/2002
The three triangles are 1
and 5, 3 and 6, and 2 and
4.
By using def and stu that is what i found when solving the problem.
77370
3508
11/26/2002
Triangles 1 and 5, triangles
3 and 6, and triangle 2 and
4 can all be put together to
form
Triangles 1 and 5 both share the similarity of the angle measurement
of 4.5 (Triangle 1 = L to J and Triangle 5 = B to A) . traingles 3
and 6 both share the angle measurement of 3.4 (Triangle 3 = g to h,
and Triangle 6 = x to y). Triangles 2 and 4 both share the angle
measurement of 6.5 (Triangle 2= line M to 0 and Triangle 4= line
RQ.)
78817
[n/a]
11/26/2002
To solve this problem, I used a spreadsheet. On this spreadsheet, I
Triangles paired are
classified triangles according to their similarities.
triangles 1 and 5, triangles
For classifing their similarities, the triangles had to have equal
2 and 4, and triangles 3 and sides, and one pair of adjacent angles that joined had to add up to
180 degrees(making a straight line).
6.
Therefore, I paired up the triangles that had equal sides, and one
78637
15764
77720
906
pair of adjacent angles added up to 180 degrees.
For triangles DEF and STU to be put together to form a larger
triangle, one of DEF's sides must be equal to one of STU's sides.
Also, one pair of their adjacent angles would have to add up to 180
degrees.(To make a straight line.)
11/27/2002
2 of 6
The biggest "hint" to me was that in the problem description it
Triangle Pairs: 2 and 4, 1
states that the traingles cannot overlap. They certainly couldn't
and 5, 6 and 3. With two
fall short of eachother either, therefore, it made the most sense
arbituary triangles DEF and that the triangles would line up perfectly, aka equally 180 degrees
and continuing the straight line. This meant that if one triangle was
STU, to be put together
acute I had to make sure to match it with a triangle that contained
they must have two angles an obtuse angle and so on. I accomplished the actual discovery of
that compliment eachother which angle fit where by simple guess and check.
(that added together equal
180 degrees) thus forming a
11/24/10 1:22 PM
The Math Forum @ Drexel University
Created
Thread
History
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Short Answer
Long Answer
Submitters School
complete line for one side
of the tr
WE GUESSED. HARD TO DO WITHOUT MOVING AROUND THE ANGLES OF THE
TRIANGLES.
11/27/2002
Traingles 2 and 4,
Traiangles 5 and 1,
Triangles 3 and 6.
11/27/2002
the answer would be having the sides would have to fit together so the sides were equal so
they would be the same lenghth so they were like 8.3" or
the sides put togeather so something like that.
they were equal so they
would have to be the same
length
11/27/2002
1,5 AND 2,4 AND 3,6 ARE
THE REQUIRED PAIRS
PAIR: 1&5
79419
[n/a]
77675
77689
16783
79420
[n/a]
AB can be superimposed on LJ since they are of same length(4.5)
angle KJL and angle ABC are linear pairs. ( since 114+66= 180)
pair: 2&6
OM and RQ can be superimposed to form tiangle PON
angles OMN AND RQP are linear pairs (since 119+61=180)
pair: 3&4
HG and XY can be superimposed to form triangle IZG
angles IHG and YXZ are linear pairs(since 90+90=180)
11/27/2002
the pairs are 1-5, 2-4, 3-6
When we look at the length of sides triangle 5 must be pair with
triangle 1 because it's the only one that has the side witch can go
together without overlapping. It's same with 2-4 too, and the
remainin 3-6 should be the last pair.
77988
[n/a]
11/27/2002
no clue
no clue
79421
[n/a]
11/27/2002
junk
1 and 5 went together, 3
and six went together and 4
and 2 went together.
79422
390
11/27/2002
triangle 1 and 5, 2 and 4, 3 i looked for equal sides between the triangles and for complementry
angles. they wernt hard to find. in order to have a pair of triangles
and 6
such as DEF and STU, that fit the qualifications, each one needs to
78753
906
77584
[n/a]
have one side equal to another and an angle complementing the other
triangle's angle.
To sort the triangles into three groups you must do several things.
First you must find two compatible triangles in which one side in
each triangle are equal length. The two triangles must be congruent
and linear. Meaning that one angle on each triangle must add up to
180 degrees or are supplementary. In this way the two triangles can
be put together to form a larger triangle.
The three pairs of triangles that I found were: Triangles 1 and 5, 2
and 4, and 3 and 6
11/27/2002
The three pairs of triangles
that I found were: Triangles
1 and 5, 2 and 4, and 3 and
6
11/27/2002
The three pairs of triangles it was simple yopu just move them around untill you get to one that
matches
that can each be put
together to form a larger
triangle are triangle 6 and 3,
triangles 1 and 5, and
triangle 2 and 4.
77979
[n/a]
11/27/2002
The sides that are pairs because they have the same angles on both
figures 1 and 5 are a pair,
sides
figures 4 & 2 are a pair, and
a figures 6 & 3
78810
[n/a]
11/28/2002
4 with 2 6 with 3 1 with 5
4 with 2 >>>>> Since >>>> Since >>>> Since
78249
[n/a]
11/29/2002
1 and 5, 2 and 4, 3 and 6
I looked at the angle to see if it's the same or not.
79431
[n/a]
11/30/2002
The triangles are : 1 and 5, If you want to get three groups of triangles and two triangles in
each group, you need to have two requirements. First, you need to
2 and 4, 3 and 6
have linear angles.
And second, the two sides, one from each
78287
[n/a]
triangle, needs to have congruent measurements. You might need to
flip the triangles around or else it might not work. This is how you
figure it out:
Triangles 1 and 5 have a congruent side of 4.5 and 4.5, and you
notice that you have to flip it in order to get the angles of 114 and
66 degrees to form linear angles. Linear angles are angles that
share a side and lie on a line and they will add up to 180 degrees.
So you flip it and rotate it until the two equal sides join the two
triangles, and you see that they will make a bigger triangle. They
are considered a group.
Next, there are triangles 2 and 4. You would also have to
flip and rotate it until it joins the two triangles together to form
3 of 6
11/24/10 1:22 PM
The Math Forum @ Drexel University
Created
Thread
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Short Answer
Long Answer
Submitters School
a bigger triangle. This time the two sides of the triangle have the
measurements of 6.5 and 6.5. The two angles that are to form a
linear angle have the measurements of 61 and 119 degrees. They will
equal 180 degrees. The two triangles will form a group.
Finally, there are the triangles 3 and 6. They will join
together to form a bigger triangle like the rest. This is the last
group of them all. This time the measurements for the two sides are
3.4 and 3.4. The two congruent angles are 90-degree angles. You
will have to flip the triangle and rotate it to get the two 90-degree
angles to form a linear angle. The sides will join and you will have
a new triangle.
11/30/2002
6, 3, and 2, are one
Triangle. 4, 1, and 5 are
another triangle.
For 6, 3, and 2,
78780
[n/a]
11/30/2002
The three pairs are GHI and
XYZ, MNO and PQR, and
LJK and ABC. Arbitrary
triangles DEF and STU can
be combined to make a
single triangle if they (1)
have at least one pair of
congruent segments, and
(2) if a linear pair is created
by two of the angles
Finding the answer to this problem is not so much about finding
additional information to solve it as it is about sifting through the
information that is already there. To find which triangles fit
together properly and which do not, all I have to do is use the
process of elimination and find which angles and sides match up.
78691
[n/a]
LJK and ABC
First, I will find LJK's counterpart. I can eliminate all choices
except MNO and ABC, because none of the choices other then them have
any congruent sides. It is impossible to match up two with
noncongruent sides, because none of the sides would fit perfectly
together, and so part of one side would rise up higher than the rest.
The resulting figure would always be a quadrilateral, or worse.
Next, I can eliminate MNO, because none of MNO's angles (that is,
those which segment MN helps form) make a linear pair with LJK's
angles (that JK helps form). If there are no linear pairs, then the
four points M, N, J, and L cannot be colinear, and do not form a
single segment. The combination of MNO and LJK would something like
this:
K/O
- - - J/N- - L
M
Angle ABC forms a linear pair with angle KJL, so JKL and ABC can be
combined to form one larger triangle.
MNO and PQR
First of all, MO and RQ are congruent, so the triangles can be matched
up exactly. Second, angle NMO and angle RQP form a linear pair, and
they are both partly formed by one of the two congruent segments. This
means that N, M, Q, and P are all colinear. Therefore, a larger
triangle is formed by segments NP, N(O/R), and (O/R)P. It looks
somewhat like this:
O/R
- - - --------------N
M/Q
P
GHI and XYZ
Since I already made two pairs, only GHI and XYZ are left, so they are
probably a pair also. Just to make sure, though, I will go through the
same steps I did last time. GH and XY are congruent, so the triangles
can be fitted together properly. Angle GHI and angle YXZ are a linear
pair, so I, H, X, and Z are all colinear. Therefore, GHI and XYZ can
be combined properly to form one triangle, like this:
G/Y
- - - -----------I
H/X
Z
DEF and STU
Two randomly selected triangles, DEF and STU, can be combined to form
a single triangle if two conditions are met. First, DEF and STU must
have two congruent sides. Second, a linear pair must be created by two
of the angles that are partly made by those congruent segments. Of
course, the two angles of that linear pair must be on separate triangles.
Reflections
When I came to the POW page to see the latest problem, I immediately
realized that Triple Tango was, conceptually, extremely simple. Then,
however, I realized the hard(er) part, which was figuring out how to
4 of 6
11/24/10 1:22 PM
The Math Forum @ Drexel University
Created
Thread
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Short Answer
Long Answer
Submitters School
word this correctly and understandably. I think the clarity of my
explanations has improved since last time, but I still need to work on
developing my communication skills. The hardest part of my explanation
was figuring out how to say 'the angles formed partly by segment
so-and-so', which I'm sure can be expressed more easily than that.
11/30/2002
triangles 1 and 5. triangles
2 and 3. triangles 4 and 6
look good
79438
[n/a]
12/01/2002
The three pairs of triangles
were GHI and XYZ, PQR
and MNO, and ABC and
JKL.
The angles of a triangle must always equal 180 degrees so, the
triangles I created have to equal 180 degrees also. The first pair
of triangles that I worked with (GHI and XYZ) was connected by a
common side length of 3.4"(inches). I added the outside angles of
tthe combined triange (64 + 26 + 66 + 24=180) which equals 180
degrees. The second pair of triangles (PQR and MNO)also had a common
side length of 6.5"(inches). I added the outside angles of the
combined triangle (39+22+29+90=180) to equal 180. With this pair I
had to flip one of the triangles over to get the shape of a
triangle. The third pair of triangles (ABC and JKL) had sides of an
equal length (4.5"). I matched the common lengthed sides and added
the outside angles of the new triangle (47+67+37+29=180) to find the
total of 180 degrees. I had to flip one of the triangles over to
make the triangle shape in this combination as well.
77539
[n/a]
DEF and STU must have a side that is the same length to create a
triangle. The four outside angles must equal 180 degrees. There are
four outside angles, because each of the individual triangles has one
one angle remaining, then another angle that on the combined triangle
has been made into a straight line, and a third angle that is
combined with the other triangles angle. The two combined angles
make angles 3 and 4 to be added. Two arbitrary triangles can be
combined in this manner.
12/01/2002
b
m
79392
[n/a]
12/01/2002
1. 6 and 2 will match
dsd
78044
[n/a]
12/01/2002
2 and 6 goes together 1
and 5 goes together 3 and
4 goes together.
i found the length of the triangle and
put them together then added them
together and divide and got the
length of the two that i choosed.
79442
6587
12/01/2002
Out of the six triangles that
are given, you can specify
them into three triangles.
The way you can do this
operation is by looking at al
the sides of the triangles,
and all the angles there are.
THe triangles that go
togheather must have at
leas
The way i found these pairs are by looking adjacent sides that are
congruent and looking for te angles that make a linear pair. Once
you have found the sides and angles that would make one big triangle,
you now hav a pair.
78428
[n/a]
12/01/2002
The triangles that go
together to form three
larger triangles are 6+3,
2+4, and 1+5.
First, I tried to find things that each triangle had in common. I
set up 6+3 at the sides XY and HG. They both equal 3.4 inches, and
the sum of all the angles is 180 degrees- the angle degrees are 82,
64, and 24.
79447
[n/a]
78560
[n/a]
Next, the angles 2+4 are a larger triangle. When attaching to MN to
QP, the sum of the angles is 180. The sum of all angles of a
triangle equals 180 degrees. The individual angle degrees of the
triangle pair are 129, 29, and 22.
The last triangle set is 1+5. When attaching LJ and AB, there are no
overlapping lines- LJ and AB both equal 4.5 inches. Since there are
no overlapping sides, and the polygon has only three sides, it is a
triangle.
5 of 6
asdf
12/01/2002
asdf
12/01/2002
The pairs are 1 and 5 2 and I just cut them out and fit them together like a puzzle
3 and 6 and 4
79450
[n/a]
12/02/2002
Line LJ from triangle one is equal to line AB from triangle five.
The triangles that go
Line GH from triangle 3 is equal to line XY from triangle 6. Line MO
together is as follows: 1&5, from triangle 2 is equal to line RQ from triangle 4.
3&6, and 2&4.
78389
[n/a]
12/02/2002
Triangle 3 and 6 will make a
triagnle when put together,
triangles 2 and 4 will make
a triangle, and triangles 1
and 5 make a triangle. If a
79034
[n/a]
triangles 3 and 6 make a triangle because side GE in triangle 3 is
3.4" and so is side XY in triangle 6, also angle H plus angle X
equals 180. Triangle 2 and 4 do the same thing due to the fact that
side OM (in triangle 2) and side RQ (in triangle 4) both equal 6.5".
also angle Q is 119 degrees, while angle M is 61 degrees, when put
together, they equal 180. Therefore, i reflected triangle 2 over
line ON and connected it to triangle 4. In a similar way, triangles
11/24/10 1:22 PM
The Math Forum @ Drexel University
Created
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Short Answer
Long Answer
Submitters School
triangle DEF has side EF
with the length of 2.3" and
angle E is 72 degrees, and
triangle STU has side TU wi
5 and 1 make a triangle when connected to eachother. in triangle 1,
side LJ is 4.5" as is line AB in triangle 5. the measure of angle J
is 114 and the measure of angle B is 66. When connected they equal
180.
12/02/2002
bkjbjb
241212
78916
[n/a]
12/02/2002
Because of matching sides
and cooresponding angles,
triangles 1 and 5, 2 and 4,
and 3 and 6 match up to
form 3 different triangles.
Triangles 1 and 5 match up to form one triangle by lining up on both
of their 4.5 sides. then the 66+144=180, a straight line. and also
the outside angles- 67+29(the newly formed angle) +47+37= 180, the
number of degrees in a triangle.
79343
[n/a]
78233
3576
Triangles 2 and 4 match up similarly, but on the 6.5 side. here 61
and 119=180 creating a straight line while 29+22+90+39=180 degrees, a
triangle.
Triangles 3 and 6 also match up. THey match up along the 3.4 side.
the two 90 degree angles form a straight line and then
26+66+64+24=180, again a triangle.
Generally speaking, in order for two triangles to match up, they
first must have a matching side. in triangles STU and DEF one of the
sides of STU must be the same legnth as that of DEF. Also in order
for the triangles to match up two of the angles (one from each
triangle) must add up to 180 degrees to form a straight line along
the bottom of the triangle. So an angle on either end of the line
that equals the other triangle must add up to 180 degrees. Once
these add up, here the triangles will match up, if they do. there is
one final stipulation, the angles must add up to 180 degrees, the
exterior angles. the two angles on the other end of the equal side
that was not used before + the two other angles(one from DEF, one
from STU) that were not on either end of the equal legnthed sides,
must equal 180 degrees total to be a triangle.
So overall to add up to a triangle there must be an equal legnth from
a side of each triangle, 2 angles on each side from different
triangles that add up to 180 degrees to form a line, and finally all
the exterior angles must add up to 180 degrees.
12/02/2002
1. I found that the three
pairs are triangles ABC and
LJK, triangles MNO and
RQP, and triangles XYZ and
HGI. 2. For triangles DEF
and STU to match up and
create a larger triangle
without overlapping, both
triangles must have at least
one congruent
1. I found out the pairs of the triangles by first figuring out that
if I wanted to only have three sides, two of the sides had to make a
straight line when they matched up. That meant that those
corresponding angles had to be supplementary. And I knew if I had
two sides that were not congruent which were matched up, an
additional side would be created, making the resulting shape a
parallelogram, not a triangle.
2. I knew that if there had to be two supplementary angles, or two
right angles, and two congruent sides for the triangles to match up
correctly, I knew all i needed was for triangles DEF and STU to both
be right triangles with at least one side congruent.
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