topic is fuzzy number
3.12. Describe real numbers close to the interval [-3, 4] by a trapezoidal fuzzy number.
Answers
A trapezoidal fuzzy number with parameters (-4, -3, 4, 5) can be used to describe real numbers close to the interval [-3, 4].
A trapezoidal fuzzy number is a type of fuzzy number that represents a range of values with a trapezoidal membership function. It is characterized by four parameters: a, b, c, and d, where a ≤ b ≤ c ≤ d.
To describe real numbers close to the interval [-3, 4] using a trapezoidal fuzzy number, we can choose the parameters as follows:
a = -4 (to include real numbers slightly less than -3)
b = -3 (the lower bound of the interval)
c = 4 (the upper bound of the interval)
d = 5 (to include real numbers slightly greater than 4)
By setting these parameters, we create a trapezoidal fuzzy number that covers the interval [-3, 4] and includes real numbers close to the edges as well.
The membership function of this trapezoidal fuzzy number will have a value of 1 between -3 and 4, indicating full membership within the interval. As the values approach -4 and 5, the membership value gradually decreases, indicating partial membership or closeness to the interval.
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Related Questions
There are 10 people waiting on standby at an airport to get on the next flight when 2 seats open up. One of the seats is in first class, and the other is in coach. What error is made in the work shown below to calculate the number of ways to choose the passengers to fill the seats
Answers
Step-by-step explanation:
As I do not have the work shown to calculate the number of ways to choose the passengers, I cannot identify the specific error made. However, I can provide some insight on how to approach this type of problem correctly.
When choosing 2 people from a group of 10, we can use combinations, which are denoted as "n choose k" and represented by the formula:
n choose k = n! / (k! * (n-k)!)
where n is the total number of items in the group and k is the number of items to be chosen.
In this case, we want to choose one passenger for first class and one passenger for coach. Therefore, we can separate the group of 10 into two subgroups: one subgroup with 1 person (for first class) and another subgroup with 9 people (for coach).
Using combinations, we can calculate the number of ways to choose 1 person from the subgroup of 1 and 1 person from the subgroup of 9:
(1 choose 1) * (9 choose 1) = 1 * 9 = 9
Therefore, there are 9 ways to choose the passengers to fill the seats.
Maggie is converting 10,560 feet to miles by using StartFraction 10,560 feet Over 1 EndFraction times StartFraction 1 mile Over 5,280 feet EndFraction. What should be Maggie’s answer?
Her answer should be One-half mile because there are 5,280 feet in a mile.
Her answer should be One-half mile because there are 10,560 feet in a mile.
Her answer should be 2 miles because there are 5,280 feet in a mile.
Her answer should be 2 miles because there are 10,560 feet in a mile.
Answers
Answer: C
Step-by-step explanation:
The answer is “ Her answer should be 2 miles because there are 5,280 feet in a mile“
(Aka: C/3.)
If you don’t belive me that’s okay, but it’s right, I just finished the pre-unit test . Hope you do good and keep those grades up!!
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Find the value of r, if P(5, r) = 2P(6, r-1)
answer choices:
a. 3
b. 5
c. 8
d. 11
Answers
The value of r in permutation P(5, r) = 2P(6, r-1) is 11. So, option d) is correct.
We know that the formula for the permutation of r objects taken from n distinct objects is P(n, r) = n! / (n-r)!. Using this formula, we can rewrite the given equation as:
5! / (5-r)! = 2 * 6! / (6-r+1)!
Simplifying this equation, we get:
5! / (5-r)! = 2 * 6! / (7-r)!
(5-r)! / 5! = (7-r)! / (2 * 6!)
(5-r)! / 5! = (7-r)! / 12
Since 5! = 120, we can simplify the left-hand side to:
(5-r)! / 120 = (7-r)! / 12
Multiplying both sides by 12, we get:
(5-r)! / 10 = (7-r)!
Multiplying both sides by 10, we get:
(5-r)! = 10 * (7-r)!
We can now manually try different values of r until we find one that satisfies the equation. Trying r = 3, we get:
(5-3)! = 10 * (7-3)!
2! = 10 * 4!
2 = 240
Since this is a contradiction, we can eliminate option (a) from the answer choices. Trying r = 5, we get:
(5-5)! = 10 * (7-5)!
1 = 20
Again, this is a contradiction, so we can eliminate option (b) from the answer choices. Trying r = 8, we get:
(5-8)! = 10 * (7-8)!
(-3)! = -10
Since the factorial of a negative number is undefined, this is not a valid solution, so we can eliminate option (c) from the answer choices. Therefore, the correct answer is (d) 11. Trying r = 11, we get:
(5-11)! = 10 * (7-11)!
(-6)! = 10 / 24
Simplifying the right-hand side, we get:
(-6)! = 5 / 12
Since the left-hand side is undefined for negative integers, we can eliminate this solution. Therefore, the only valid solution is r = 11, which we can confirm by checking that both sides of the equation are equal when r = 11. So, the correct answer is option (d).
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To develop an understanding of, and ability to calculate, molecular energy levels.
In diatomic molecules, there are two different ways that the molecule may move without its center of mass moving:
rotating around its center of mass and
vibrating as if the two atoms are connected by a spring.
Energy may be added to the molecule by increasing the speed of rotation or the amplitude of the vibrations. As you should expect from quantum mechanics, energy must be added to molecules in specific quantities. Two of the solutions of the Schrödinger equation that you may have seen before--the hydrogen atom and the harmonic oscillator--will be useful in the study of molecules.
In looking at the Schrödinger equation for hydrogen, you learned that one important aspect of hydrogen is that it has a spherically symetric potential (i.e., the potential energy of the electron in a hydrogen atom depends only on its distance from the nucleus). This gives rise to the following equation for the allowed values of L2:
L2=l(l+1)ℏ2(l=0,1,2,3…),
where L is the angular momentum. When we look at the rotation of diatomic molecules, we also have a spherically symmetric potential energy function, specifically U(r)=0. Since this is the case, we can use the same equation for the angular momentum states that we used with hydrogen.
Answers
Diatomic molecules can move through rotation and vibration. Quantum mechanics quantizes energy, and the Schrödinger equation provides solutions for studying molecular energy levels.
When examining molecular energy levels, diatomic molecules exhibit rotational and vibrational motions independent of their center of mass. In quantum mechanics, energy is quantized, meaning it can only be added or subtracted in specific discrete quantities.
The Schrödinger equation provides solutions for various quantum systems. Two solutions, the hydrogen atom and the harmonic oscillator, are particularly useful for studying molecules. The hydrogen atom has a spherically symmetric potential energy, which allows us to determine the allowed values of angular momentum (L) using the equation L^2 = l(l + 1)ℏ^2, where l represents different angular momentum states (l = 0, 1, 2, 3, ...).
Similarly, diatomic molecules have a spherically symmetric potential energy function U(r) = 0 for rotation. As a result, we can utilize the same equation for the allowed angular momentum states as in the case of the hydrogen atom, enabling us to analyze and understand the rotational energy levels of diatomic molecules.
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In 1992 a gigabyte cost $3000. In 2012 the gigabyte price decreased by 97%. What was the cost of a gigabyte in 2012
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Find the value of x to make the following equation true.(3^2)^3 x 3^x = (3^7x3^3)/3^11Ax = 1Bx=-7сX = 8DX = -6
Answers
Given the expression:
\((3^2)^3\cdot3^x=\frac{3^7\cdot3^3}{3^{11}}\)notice that on the left side, if we simplify, we have the following:
\((3^2)^3\cdot3^x=3^6\cdot3^x=3^{x+6}\)and on the right side, we have:
\(\frac{3^7\cdot3^3}{3^{11}}=\frac{3^{7+3}}{3^{11}}=\frac{3^{10}}{3^{11}}=3^{10-11}=3^{-1}\)then, if we equate both expression we have that:
\(3^{x+6}=3^{-1}\)then, this must mean that the exponents are equal. This means the following:
\(x+6=-1\)solving for x we get:
\(\begin{gathered} x+6=-1 \\ \Rightarrow x=-1-6=-7 \\ x=-7 \end{gathered}\)therefore, x = -7
Melissa has 120 vanilla cake pops to sell. Each vanilla cake pops is covered with one topping. 1/2 of the cake pops are covered with chocolate sprinkles. 1/3 of the cake pops are covered with strawberry sprinkles. * the rest are covered with green sprinkles. How many cake pops are covered with green sprinkles?
Answers
Answer:
The Answer is 20 cake pops are covered with green sprinkles.
Step-by-step explanation:
So if you have 1/2 choclate, 1/3 strawberry, and the rest are green, you first need to convert the Chocolate and the Strawberry into the same fraction. As shown:
Chocolate: 1/2=3/6
Strawberry:1/3=2/6
The rest are Green sprinkles.
So, your equation would be:
Chocolate sprinkles + Strawberry Sprinkles + Green Sprinkles = Total
And their are 5/6 of Chocolate and Strawberry Sprinkles...
That would mean 100 Chocolate and Strawberry Sprinkles!
Because 1/6 of 120 is 20 and multiply that by five and you have 100...
Now that we have that, and we know the rest are green...
we just do 120-100=20
So their you go!
Sorry its long but hope it helps! <3
Which prize is worth more? Explain your reasoning.
a) a prize on March 21, if $5 is given on March 1, five times as much on March 2 ($25), five times as much on March 3 ($125), and so on, to March 21
b) a prize of $9.5 billion
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a parabola goes through and . write a system of equations that you could solve to find the equation of the parabola.
Answers
To find the equation of a parabola that passes through two points and a third point, we need to write a system of three equations in three variables (a, b, and c) using the standard form of the parabolic equation, and then solve for the variables.
To find the equation of a parabola that passes through two points, we can use the standard form of a parabolic equation: y = ax^2 + bx + c. Since we have two points, (x1,y1) and (x2,y2), we can write two equations:
y1 = ax1^2 + bx1 + c
y2 = ax2^2 + bx2 + c
We need to solve for a, b, and c. One way to do this is to eliminate c by subtracting the second equation from the first:
y1 - y2 = a(x1^2 - x2^2) + b(x1 - x2)
Now we can use the fact that the parabola passes through a third point, (x3,y3), to write another equation:
y3 = ax3^2 + bx3 + c
We can substitute c from the first equation into this equation:
y3 = ax3^2 + bx3 + y1 - a(x1^2 - x2^2) - b(x1 - x2)
Now we have three equations and three unknowns (a, b, and c), which we can solve using algebra or matrix methods. Once we have the values of a, b, and c, we can plug them into the standard form of the parabolic equation to get the equation of the parabola that passes through the three points.
The resulting equation will be the equation of the parabola that passes through the given points.
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Geometry help please!! 20 points
Answers
Answer:
Step-by-step explanation:
Opposite angles of a cyclic quadrilateral are supplementary, so (6x+72)+3x=180
\((6x+72)+3x=180\\9x+72=180\\9x=108\\x=12\)
I only have 10 minutes. Will give brainliest
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The value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔.
What are similar shapesSimilar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.
The side A'E' corresponds to the side A'E' and also E'D' corresponds to the side ED so;
(7). A'E'/AE = E'D'/ED
x/10 = 6/9
x = (10 × 6)/9 {cross multiplication}
x = 20/3
x = 6⅔
Therefore, the value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔
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How much better or worse would it be to use the average nominal annual rate for two years with continuous compounding? Part III (40 Points) Suppose there are two banks in your town, Happy Bank and Trusty Bank Happy Bank is oşering semiannual compounding at a nominal annual rate of 604 percent. Trusty Bank is ofering monthly compounding at a nominal annual rate of 6.00 percent (In the questions that follow, it it is helpful, suppose the initial amount of money is $1000) 1. Which is a better deal if you are going to deposit money for three years? Explain your reasoning 2. Would your answer change if you were going to deposit money for nine years? Brieáy, why or why not? 3. Would your answer change if you were going to borrow money for three years? Brieáy, why or why not? 4. How long does it take for your money to triple at Trusty Bank?
Answers
2 If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period.
3 The future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81.
3 it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.
When comparing the two banks, it is important to note that Happy Bank is offering semiannual compounding while Trusty Bank is offering monthly compounding. To compare the two rates on an equal basis, we need to convert them into their equivalent annual rates with continuous compounding, which takes into account compounding frequency.
The formula for the continuous compounding rate is e^(r/n)-1, where r is the nominal rate and n is the compounding frequency. For Happy Bank, the continuous compounding rate would be e^(0.06/2)-1 = 0.0294, or 2.94%. For Trusty Bank, the continuous compounding rate would be e^(0.06/12)-1 = 0.0049, or 0.49%.
Using these rates, we can calculate the future value of $1000 over three years. At Happy Bank, the future value would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Happy Bank is the better deal for a three-year deposit.
If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period. However, without additional information about compounding frequency and rates, we cannot determine which bank would be the better deal.
If we were to borrow money for three years, the calculations would be similar but the direction would be reversed. At Happy Bank, the future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Trusty Bank would be the better option for a three-year loan.
To determine how long it takes for the money to triple at Trusty Bank, we can use the formula FV = PV * e^(rt). If we start with $1000 and want to find when it will triple, we can set FV = $3000 and solve for t. This gives t = ln(3)/0.06 = 11.55 years. Therefore, it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.
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7 Chris needs to cut a roll of twine into 16 equal lengths for a
project. If the roll of twine measures 900 inches, how long
will each length of twine measure?
Answers
Answer:
I am pretty sure it is 56 because all you have to do is dvided and it comes out to 56.25 but you cant have .25 because that is not an equal peice so yeah I think it is 56
Answer:56.25
Step-by-step explanation:I had same problem it was correct
income consists of $320 per week plus a commission of 6% of her sales. write an algebraic expression for utako's weekly income, i , in terms of her sales, s .
Answers
The algebraic expression for Utako's weekly income in terms of her sales can be written as i = 320 + 0.06s where i is the weekly income and s is the sales.
The given algebraic expression i = 320 + 0.06s represents Utako's weekly income in terms of her sales. The expression consists of two parts - a fixed component of $320 per week and a variable component of 6% commission on her sales.
To evaluate Utako's weekly income for a particular value of sales, we simply substitute that value of s in the expression and calculate the corresponding value of i. For example, if her sales are $5000 in a week, then her weekly income would be:
i = 320 + 0.06(5000) = 320 + 300 = $620
Similarly, for any other value of sales, we can calculate her weekly income using this expression. This equation is useful for Utako to estimate her income based on her sales and to plan her finances accordingly.
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What is a fallacy? Give examples of fallacies and describe how the argument is deceptive.
What is a fallacy?
A.
A fallacy is the study of the methods and principles of reasoning.
B.
A fallacy is a fact or assumption used in an argument to support a conclusion.
C.
A fallacy is a deceptive argument. It is an argument in which the conclusion is not well supported by the premises.
D.
A fallacy is a set of facts or assumptions, called premises, to support a conclusion.
Please help!
Answers
The answer to this question is option c. A fallacy is a deceptive argument. It is an argument in which the conclusion is not well supported by the premises.
A fallacy is a false or untrue statement. The argument in a fallacy is deceptive because the reasoning behind it makes the argument invalid.
A fallacious argument is an argument that is actually different from what it presents itself to be.
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What is the solution y 2 3x 3 x =- 2?
Answers
The solution of the equation y = (2/3)x + 3 is 5/3
The given equation is
y = (2/3)x + 3
The slope of the line is the change in y coordinates with respect to the change in x coordinates.
This is the linear equation in the the slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept
y is the y coordinates
x is the x coordinates
The value of x = -2
Substitute the value of x in the equation
y = (2/3) × -2 + 3
Do the arithmetic operations
= -4/3 + 3
Add the numbers
= 5/3
Therefore, the solution is 5/3
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the solution of the equation y = (2/3)x + 3x, when x = -2?
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Find an equation of the line that has a slope of -1 and a y intercept of 5. Write your answer in the form
y = mx + b.
y =
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\(y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
A bakery offers a sale price of 2.55 for 4 muffins.what is the price per dozen?
I hope someone answers fast
And explain what you did
Answers
Answer: $7.65 for a dozen/12
Step-by-step explanation: 2.55 x 3
x – 3y 32
Does this inequality have a solid or dashed boundary line?
Answers
Step-by-step explanation:
It doesn't have neither the greater than or equal to or less than or equal to signs so
A nutrition company is marketing a low calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories.
If c represents the number of calories and b represents the number of brownies write a proportional relationship involving c and b and solve it for c.
Answers
The relationship between the variables c and b is c = \(\frac{50}{3}b\)
What is Variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
if c ∝ b
Then,
c = kb where k is a constant
When c = 50, b = 3
substituting into the equation above,
50 = 3k
k = 50/3
substitute k into the equation
c = \(\frac{50}{3}b\)
In conclusion c is related to b by the equation c = \(\frac{50}{3}b\)
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Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 i. Which statement describes the number and nature of all roots for this function?.
Answers
The correct option is f(x) has three real roots and two imaginary roots.
Given
Three roots of a fifth-degree polynomial function f(x) are –2, 2, and 4 i.
Complex conjugateThe complex conjugate of a complex number is the number with an equally real part and an imaginary part equal in magnitude but opposite in sign.
It is given that the roots of the fifth-degree polynomial function are -2, 2, and 4+i.
Since the degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.
According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).
Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).
From the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.
Therefore, the correct option is f(x) has three real roots and two imaginary roots.
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Answer:
f(x) has three real roots and two imaginary roots.
Step-by-step explanation:
on edge 2023
What is the volume of the prism below? 8 7 5
Answers
Answer:
V=280
Step-by-step explanation:
V=whl
V=(8)(7)(5)
V=280
Answer:
140 units ^3
Step-by-step explanation:
a p e x
I don’t know how to do this HELP
Answers
Answer:
Both
Step-by-step explanation:
5+3+4=
12
3+1+1=
5
1+1=
2
1=
1
The line plot shows this data for each number.
PLEASE HELP!!! Whoever solves this word problem for me within 15 minutes gets 90 points and gets marked brainliest!
Answers
283
She can spend $283 or less
Answer:
$283 and or algebraic form 458 - x ≥ 175
Step-by-step explanation:
If you subtract 458-175 you get 283 so that how much Megan can spend.
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number
Answers
Answer:
I believe the answer would be 10/40. First, I simplified all of the given rations. You do this by finding the two numbers greatest common factor. For example, 3/12, 3 goes into 3 once and 3 goes into 12 four times. So that ratio would be 1/4. If you continue the pattern you would get 1/4 for all of them. Therefore, 10/40 would be correct since it's ratio would also be 1/4.
Step-by-step explanation:
A local produce stand has eight pumpkins on display the diameters of the pumpkin in inches are given in the table
Answers
SOLUTION
We will be pairing the pumpkins as follows
AB, CD, EF and GH
For AB, we have
\(\begin{gathered} 16\frac{1}{2}\div5\frac{1}{2} \\ \frac{33}{2}\div\frac{11}{2} \\ \frac{33}{2}\times\frac{2}{11} \\ =\frac{33}{11} \\ =3 \end{gathered}\)Hence B is 3 times larger than A
For C and D, we have
\(\begin{gathered} 41\frac{1}{4}\div8\frac{1}{4} \\ \frac{165}{4}\div\frac{33}{4} \\ \frac{165}{4}\times\frac{4}{33} \\ =\frac{165}{33} \\ =5 \end{gathered}\)Hence D is 5 times larger than C
E and F, we have
\(\begin{gathered} 13\frac{3}{4}\div3 \\ \frac{55}{4}\div\frac{3}{1} \\ \frac{55}{4}\times\frac{1}{3} \\ =\frac{55}{12} \\ =4.5833333333 \\ =4.583 \end{gathered}\)Hence E is 4.583 times larger than F
And the last G and H, we have
\(\begin{gathered} 22\frac{3}{4}\div10\frac{1}{2} \\ \frac{91}{4}\div\frac{21}{2} \\ \frac{91}{4}\times\frac{2}{21} \\ =\frac{91}{21\times2} \\ =\frac{91}{42} \\ =2.167 \end{gathered}\)Hence G is 2.167 times larger than H
HELP ME AND GET POINTS!!!!!
Answers
Answer:
7 13
Step-by-step explanation:
Answer:
C. 7 and D, 13 are prime.
Hope it will help :)
a social security number contains nine digits, such as 010-50-0257. how many different social security numbers can be formed?
Answers
The total number of social security numbers that are possible are 900,000,000.
In the social security number first digit can only fall between 1 and 9, leaving us only nine options because the first three digits cannot all be zeros. There are still 10 possibilities for each of the second and third digits because they may both still be any integer between 0 and 9.
Therefore, the total number of different social security numbers that can be formed is using the combinations,
= 9 × 10⁸
= 900,000,000
So, there are 900,000,000 different possible social security numbers.
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Someone help me pleaseeee
Answers
For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
What is right triangle?A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.
The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.
Given a right triangle with base = 8 and an angle = 24°
Using angle sum property of triangle
24 + 90 + angle L = 180
L = 66°
Using Sohcahtoa
Tangent: tan(θ) = Opposite / Adjacent
tan(24°) = LK/8
0.445 = LK/8
LH = 8 × 0.445
LK = 3.56
LM = \(\sqrt{MK^2 + LK^2}\)
LM = \(\sqrt{8^2 + 3.56^2}\)
LM = 8.75
Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
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proving triangle similarity
could someone explain this to me? kinda confused
Answers
Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.
What is the AA Similarity Theorem?The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.
With the information given, the proof that shows that the two triangles are similar as as follows:
Statements Reasons
1. ∠QPR ≅ ∠STR 1. Given
2. QR ⊥ PT 2. Given
3. ∠QRP ≅ ∠SRT 3. def. of perpendicular
4. ΔPQR ~ ΔTSR 4. AA Similarity Theorem
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