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Check this out.
http://www.math.washington.edu/~king/coursedir/m444a03/notes/congruence%20html/tri-congruence-summ.html
That includes proof for the congruence criterias.
I'll do them later probably.
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You are quick at finding 13=...
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Well if we have a perpendicular bisector as the diagonal, then by SAS we can see that they are congruent.
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Oh okay then. So because the sides and angles coincide (ABC and DEF) making them congruent, that would be a valid proof for Side-Angle-Side? Anyways, thank-you both.
For example, to prove Side-Side-Side, using Side-Angle-Side, we just make two triangles such that they make a kite (being diagonal). That proves that the triangles are congruent.
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13=2/2+3*(0+4)
Well isn't SAS just an axiom? How do you prove that: If 2 sides and angles in a triangle are congruent to two sides and angles of another triangle, the triangles are congruent. Like take 2 triangles: ABC, DEF. If AB=DE, AC=DF and angle A = angle D, the triangles ABC and DEF are congruent.
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13=2-2-2+7+8
So I was just wondering, is there a proof to SAS?
According to NewScientist, Cooper will recieve $3000.
Yesterday, our prof. asked me to name the criterion for triangle congruences which I did. Then he asked me to provide the proof for them which I also did (except SAS of coufrse). He then scolded me and replied that there is a proof for SAS. Until then I was pretty sure that it was an axiom which we use to prove the other criterias.
Some physics professor that must have been. This year the class average for the midterm has been 64% for which my teacher was extremely mad at. The weird thing is, he behaved slightly better with the students in the mid-70%s rather then my friends and I who were in the 90%s range. That would mean he preferred the experimental learners then the conceptual ones.
I recently saw videos of Arthur Benjaman (the "Mathemagician") and saw him calculate day of the week in 3 seconds given the date and month. I checked out Zeller's congruence and then found an algorithm which isextremely simple.
http://www.gregmiller.net/astro/dow.html
I do believe that they offer a 5000$ prize to the dicsoverer.
Since Σ(d - d)2 = 270, we get the sample mean difference.
Welcome to the forum. Frankly I did not manage to read your inordinately long post though...
Twenty-two students were randomly selected from a population of 1000 students. The sampling method was simple random sampling. All of the students were given a standardized English test and a standardized math test. Test results are summarized below.
Student English Math Difference, d (d - d)2
1 95 90 5 16
2 89 85 4 9
3 76 73 3 4
4 92 90 2 1
5 91 90 1 0
6 53 53 0 1
7 67 68 -1 4
8 88 90 -2 9
9 75 78 -3 16
10 85 89 -4 25
11 90 95 -5 36
Student English Math Difference, d (d - d)2
12 85 83 2 1
13 87 83 4 9
14 85 83 2 1
15 85 82 3 4
16 68 65 3 4
17 81 79 2 1
18 84 83 1 0
19 71 60 11 100
20 46 47 -1 4
21 75 77 -2 9
22 80 83 -3 16
Σ(d - d)2 = 270
d = 1
What is the 90% confidence interval for the mean difference between student scores on the math and English tests? Assume that the mean differences are approximately normally distributed.
1+1.3
That is the answer I am getting, but am not sure.
Poor statistician...
March 16th 1999.
Welcome back.
14 in March.