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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Why cant you use AA or ASS properties to prove triangles congruent?
There is no AA congruence property. Two triangles with the same angles are similar, but need not be congruent. In other words, they are the same 'shape' but different sizes. For example, an equilateral triangle can be big or small, but all equilateral triangles have 60 degree angles.
Although it is often said that there is no ASS congruence theorem in geometry, this isn't quite true. For prescribed values of angle, side, side, there are at most two different "congruence classes" of triangles realizing these values. In other words, there are really only at most two different types of triangles with those given values: any other triangle with the same values is congruent to one of those two.
When you study trigonometry, you will learn something called the "Law of Sines." It will give you at most two possible values for the angle opposite the middle S in aSs (they are supplementary to each other.) Then the ASA congruence theorem can be applied.
Prove that cube root of 7 is an irrational number?
The proof is by the method of reductio ad absurdum. We start by assuming that cuberoot(7) is rational. That means that it can be expressed in the form p/q where p and q are co-prime integers. Thus cuberoot(7) = p/q. This can be simplified to 7*q^3 = p^3 Now 7 divides the left hand side (LHS) so it must divide the right hand side (RHS). That is, 7 must divide p^3 and since 7 is a prime, 7 must divide p. That is p = 7*r for some integer r. Then substituting for p gives, 7*q^3 = (7*r)^3 = 343*r^3 Dividing both sides by 7 gives q^3 = 49*r^3. But now 7 divides 49 so 7 divides the RHS. Therefore it must divide the LHS. That is, 7 must divide q^3 and since 7 is a prime, 7 must divide q. But then we have 7 dividing p as well as q which contradicts the requirement that p and q are co-prime. The contradiction implies that cuberoot(7) cannot be rational.
In the worst case, each package of cards contains 20 different cards, and each package is different than any other package. This means that, if there are 550 different cards, it would take 27.5 packages to contain all 550 cards. Since you cannot purchase a half package, you would have to purchase 28 packages to ensure that you get more than one of the same card.
Is The converse of a biconditional statement is always true?
No, not always. It depends on if the original biconditional statement is true. For example take the following biconditional statement:
x = 3 if and only if x2 = 9.
From this biconditional statement we can extract two conditional statements (hence why it is called a bicondional statement):
The Conditional Statement: If x = 3 then x2 = 9.
This statement is true. However, the second statement we can extract is called the converse.
The Converse: If x2=9 then x = 3.
This statement is false, because x could also equal -3. Since this is false, it makes the entire original biconditional statement false.
All it takes to prove that a statement is false is one counterexample.
What can be said about the relationship between triangle and circles?
- Exactly one circle can be inscribed in a given triangle.
- Many triangular shapes can be inscribed in a given circle.
What is the derivative of cos lnx?
This is a chain rule question.
Let u = ln(x)
d{cos[ln(x)]}/dx = (d[cos(u)]/du)*(du/dx) = -sin(u)*(du/dx) = -sin[ln(x)]*d[ln(x)]/dx = -sin[ln(x)]/x
What are 5 geometry terms that all begin with the same letter?
- point
- plane
- polygon
- Pythagorean Theory
- pentagon
- protractor
Why congruence is a special case of similarity?
Term similar is more wide than term congruent. For example: if you say that two triangles are congruent that automatically means that they are similar, but if you say that some two triangles are similar it doesn't have to mean that they are congruent.
angle SKL = angle CGFangle KLS = angle GFC
angle LSK = angle FCG
SK = CF
KL = FG
SL = CG.
Is ABC DEF If so identify the similarity postulate or theorem that applies?
cannot be determined
Similar-AA
true
Which of the following are accepted withoiut proof in a logical system?
The question asks about the "following". In those circumstances would it be too much to expect that you make sure that there is something that is following?
9th edition by thomas and finney
What is the Converse of isosceles triangle theorem?
The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.
How do you understand trigonometry?
It is simple the study of triangles: the properties of their sides and angles. This is then extended to other, more complicated polygons and polyhedra, but the basis is still the triangle.
Can one chicken lay 2 eggs in one day?
They can, but is unlikely. Most hens lay a egg every 25 hours.
Actually, no. There are currently no breeds that will produce two eggs within 24 hours. Many breeds actually take longer than 24 hours to lay an individual egg.
1:2
What is the tens digit of the product 1 to 99?
0. There are 9 multiples of 10 between 1 and 99, so 99 factorial is divisible by at least the 9th power of 10. Therefore the last 9 digits are 0.
It is helpful (not help full) because the two triangles formed by either diagonal are congruent.
It does indeed seem like there should be a rule for adding radicals. There are rules for adding, subtracting, multiplying, and dividing whole numbers, and there are rules for multiplying and dividing radicals. However, there is no "rule" for adding radicals. For example, sqrt(2)+sqrt(3) does NOT equal sqrt(5), sqrt(6), or any other "radical" you could think of. In a professional research paper (and on any exam you may take) an answer of sqrt(2)+sqrt(3) would be a proper answer (assuming it is correct). However, a number like sqrt(4)+sqrt(1) can be simplified. This is simply 3.
Essentially, if a radical has no "nice square root" it cannot be simplified.
It is important to note, however, that an expression like sqrt(2)+sqrt(8) can be simplified. Since sqrt(8)=sqrt(4)sqrt(2)=2sqrt(2), the desired quantity could be simplified to 3sqrt(2).
I hope this was quite informative, and in time to help!
What is 3 dimensional worksheet?
It is normally a workbook that is 3 dimensional rather than a worksheet. Each worksheet consists of cells laid out in rows and columns. These are the first two dimensions. However, you can also have a "stack" of worksheets where ranges can be defined in terms of the same cell in a set of worksheets. This, then, is the third dimension.
What is the proof to this G therefore H v not H?
Suppose H is true the H or not H is true.Suppose H is false. Then not H is true and therefore H or not H is true.
Therefore, in either case, the conclusion "H or not H" is always true.
A conditional statement is false if the condition is true but the conclusion is false. Here the latter cannot happen and so the conditional statement is always true.
