The question appears to be about finding the midpoint of segment AH, which involves dividing the segment into two equal parts, either by measurement or by averaging the coordinates of A and H if available.
Explanation:The question seems to be asking about identifying the midpoint of a line segment in a geometric construction. However, the provided text alludes to various geometric proofs and theorems, rather than directly providing information about finding midpoints.
To find the midpoint of segment AH, one would need to measure the length of AH and then divide it by 2 to find the center point. If the points A and H are on a coordinate plane, the midpoint can be found by calculating the average of the x-coordinates and the y-coordinates of the endpoints A and H. Without specific coordinates or measurements, a more detailed answer cannot be provided.
The midpoint of AH is (0, 4).
Let's assign coordinates to the points A and H to make it easier to calculate the midpoint. Suppose A is at (x1, y1) and H is at (x2, y2).
The formula for finding the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is:
[tex]M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)[/tex]
If we assume A is at (0, 0) and H is at (0, 8) (since H is directly 'below' A on a vertical line), the coordinates are as follows:
A = (0, 0)
H = (0, 8)
Now, applying the midpoint formula:
[tex]M = \left( \frac{0 + 0}{2}, \frac{0 + 8}{2} \right) = (0, 4)[/tex]
what’s the measure of the missing angles?
Answer:
Angle 1 equals 90 degrees. Angle 2 equals 38 degrees.
Step-by-step explanation:
Angle 1 is at the cross of two perpendicular lines, making it 90 degrees. Angle 2 can be found by making the two equal side lengths and the middle line into one triangle. This means that two of the angles are 52 degrees. This leaves 76 degrees to be split in the triangle. The middle line cuts the angle in half, making it 38 degrees
what is the following qoutient? 3√8/4√6
Answer:
3 sqrt(3)
----------- or -----------
2 sqrt(3) 2
Step-by-step explanation:
3 sqrt(8)
-----------------
4 sqrt(6)
3 sqrt(4*2)
-----------------
4 sqrt(3*2)
We know that sqrt(ab) = sqrt(a) sqrt(b)
3 sqrt(4) sqrt(2)
------------------------
4 sqrt(3) sqrt(2)
Canceling the sqrt(2) and sqrt(4) is 2
3*2
----------
4 sqrt(3)
3
-----------
2 sqrt(3)
We can simplify the answer be multiplying by sqrt(3)/sqrt(3)
3 sqrt(3)
----------- * ----------
2 sqrt(3) sqrt(3)
3 sqrt(3)
-----------
2 *3
sqrt(3)
-----------
2
Solve for x. Can somebody help me? I don’t understand how to do this.
[tex]-1=\dfrac{5+x}{6}\\\\-6=5+x\\\\x=-11[/tex]
"Solve for x" means get an equation that says " X = something ". It has nothing but X all alone on one side, and the other side tells exactly what X is equal to.
How do you get such an equation ?
-- Take what they gave you in the question.
-- Do anything you want on one side of it, to get X all by itself on that side.
BUT . . .
-- Whatever you do to one side, you must immediately do the same thing on the other side.
Here's how that goes:
Given in the question: -1 = (5 + X) / 6
Multiply each side by 6 : -6 = 5 + X
Subtract 5 from each side: -11 = X
And there you are. It's over almost as soon as it started.
Did do this right using PEMDAS
8/2(2+2)
Solve:
8/2(4)
8/2*4
8/8
=1
Answer:
nope its not. You should count it like this (8 / 2) * (2 + 2)
Step-by-step explanation:
(8 / 2) * (2 + 2)
4 * 4
16
[tex]\text{Hey there!}[/tex]
[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]
[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]
[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]
[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
the product of 3 different positive integers is 8 . What is the sum of these integers ?
A : 7
B : 11
C : 13
D : 14
The sum of three positive integers given their product is 7, analyze the factors of the product and sum them up.
The sum of three positive integers whose product is 8 can be found by analyzing the factors of 8.
Given that the product of three different positive integers is 8, the three integers are 1, 2, and 4. Therefore, the sum of these integers is 1 + 2 + 4 = 7.
Six more than the quotient of four and a number xxx.
Answer:
[tex]\large\boxed{\dfrac{4}{x}+6}[/tex]
Step-by-step explanation:
Six more than the quotient of four and a number x:
[tex]\dfrac{4}{x}+6[/tex]
Answer:
[tex]\frac{4}{x}+6[/tex]
Step-by-step explanation:
We have been given a word phrase. We are supposed to represent our given word phrase into an algebraic expression.
The quotient of four and a number x will be 4 divided by x. We can represent this information in an expression as:
[tex]\text{Quotient of four and a number }x=\frac{4}{x}[/tex]
Six more than the quotient of four and a number x would be [tex]\frac{4}{x}+6[/tex]
Therefore, our required expression would be [tex]\frac{4}{x}+6[/tex].
A circular pie has an area of 706.5 cm2. What is the radius of
the pie?
A)225cm
B)30cm
C)15cm
D)112.5
[tex]\large\boxed{\text{C}).\,15\,\text{cm}}[/tex]
Step-by-step explanation:In this question, we're trying to find what the radius of the circular pie is.
In this question, we know that the area of the pie is 706.5 cm²
We can use the area to find our radius.
We would use the formula [tex]r=\sqrt\frac{A}{\pi}[/tex] to find the radius.
R= radius
A = Area
Your equation should look like this:
[tex]r=\sqrt\frac{706.5}{\pi}[/tex]
Now, you will solve.
[tex]r=\sqrt\frac{706.5}{\pi}\\\\\text{You can make it simpler by turning}\, \pi\,\text{into} 3.14\\\\r=\sqrt\frac{706.5}{3.14}\\\\\text{Divide 706.5 by 3.14}\\\\r=\sqrt225\\\\\text{Now, get the square root of 225}\\\\r=15[/tex]
When you're done solving, you should get 15.
This means that the radius of the pie is 15 cm.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Final answer:
To find the radius of the pie given its area of 706.5 cm², we use the formula A = πr² and solve for r, yielding an approximate radius of 15 cm. This corresponds to option C) on the given list.
Explanation:
To find the radius of the pie given its area, we can use the area formula for a circle: A = πr². Since the area of the pie is given as 706.5 cm², we can rearrange the formula to solve for the radius (r).
The rearranged formula to solve for the radius is: r = √(A/π).
Substituting the given area, we have:
r = √(706.5 cm²/π)
r = √(706.5/3.14159265359)
r ≈ √(225)
r ≈ 15 cm
Therefore, the radius of the pie is approximately 15 cm, making option C) the correct answer.
-2y+x=2y-8 what is the y-int and x-int?
Answer:
x-intercept (-8,0)
y-intercept (0,2)
Step-by-step explanation:
To find the x-intercept, you set y equal to 0.
Like this:
-2(0)+x=2(0)-8
0 +x=0 -8
x= -8
So the x-intercept is (-8,0).
To find the y-intercept, you set x equal to 0.
Like this:
-2y+0=2y-8
-2y =2y-8
Subtract 2y on both sides
-4y=-8
Divide both sides by -4
y=2
So the y-intercept is (0,2)
Decide whether each of the following statements is true. If false, demonstrate why.
a. 6!= 6.5!
b. 4! + 2! = 6!
C. 6!/3!=2!
Answer:
a is the only true one if you meant 6 times 5!
Step-by-step explanation:
Before we being
n!=n*(n-1)*(n-2)*...(3)(2)(1)
Example: 5!=5(4)(3)(2)(1) and 10!=10(9)(8)(7)(6)(5)(4)(3)(2)(1)
Yes that operation is multiplication.
a) Does 6!=6*5!
Let's see
6!=6*5*4*3*2*1
5!=5*4*3*2*1
So 6*5!=6(5*4*3*2*1)=6*5*4*3*2*1=6!
So true!
b) Does 4!+2!=6! ?
4!=4(3)(2)(1)
2!=2(1)
6!=6(5)(4)(3)(2)(1)
Does
4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)
24 +2 =720
26=720 (this is not true)
So 4!+2! is not 6!
c) Does 6!/3!=2! ?
6!=6(5)(4)(3)(2)(1)
3!=3(2)(1)
If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6(5)(4).
So the question becomes is 6(5)(4)=2!
2!=2(1)=2
6(5)(4)=2?
No way! That is saying 120=2 which is not true.
The evaluations of the statements are: (a) false because non-integer factorials are not defined, (b) false because the sum of 4! and 2! does not equal 6!, and (c) false because 6! divided by 3! is 120, not 2!.
Explanation:Let's evaluate each statement one by one.
a. 6!= 6.5!This statement is false. The factorial function is defined for non-negative integers. Since there is no definition for non-integer factorial such as 6.5!, this comparison is invalid. A correct statement may involve only integer factorials.
b. 4! + 2! = 6!This statement is also false. To show this, let's calculate each factorial:
4! = 4 x 3 x 2 x 1 = 242! = 2 x 1 = 26! = 6 x 5 x 4 x 3 x 2 x 1 = 720Adding 4! and 2! gives 24 + 2 = 26, which is not equal to 6! (720). This statement could be corrected by finding two factorials that add up to another factorial, if such a pair exists.
c. 6!/3!=2!This statement is false. By calculating the factorials, we have:
6! = 7203! = 6Therefore, 6!/3! is equal to 720/6, which simplifies to 120, not 2 (which is the value of 2!). The correct statement is 6!/3! = 120.
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Which expression is equivalent to 3 square root x^5y
The correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y
Therefore, after simplification, the equivalent expression to 3√x⁵y is x⁵/³y.
The expression 3√x⁵y represents the cube root of x⁵y. To simplify this expression, let's break it down step by step.
First, we can express 3√x⁵y in exponential form:
3√x⁵y =(3x⁵y)¹/³
Using the property (ab)ⁿ=aⁿ⋅bⁿ, we can separate the terms inside the cube root:
(3x⁵y)¹/³ =3(x⁵/³, y¹/³)
Now, let's look at the options provided:
a. x⁵/³y
b. x⁵/³y¹/³
c. x⁵/³y
d.x⁵/³y³
Comparing the simplified expression 3√x⁵y=3(x⁵/³, y¹/³) to the given options: correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y.
Suppose Q and R are independent events. Find P (Q and R) if P(Q) = 4/7
and P(R) = 1/2
Answer:
2/7
Step-by-step explanation:
If two events A and B are independent, then P(A and B)=P(A)P(B).
So since Q and R are independent, then P(Q and R)=P(Q)P(R).
Let's substitute and evaluate:
[tex]P(Q\text{ and }R)=P(Q)\cdot P(R)=\frac{4}{7} \cdot \frac{1}{2}=\frac{4}{14}[/tex].
Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:
4/14=(4/2)/(14/2)=2/7
Find the product (7v+8)(4v2 - 8v+1)
7v(4v2-8v+1)+8(4v2-8v+1)
28v3-56v2+7v+32v2-64v+8
Answer= 28v3 -24v2 -57v +8
I need help please.
Answer:
Step-by-step explanation:
1/5 + 1/5^-2
1/5 + 1/25
1/5 = 5*1 / 5*5
5/25 + 1/25
6/25 which cannot be reduced or changed.
FGH is a right triangle. True or False?
Your mouse pointer is covering the number at the hypotenuse, but I assume that it is 10.
We can test to see if the triangle is a right angled triangle by using Pythagoras' Theorem. This is because the Pythagorean Theorem only works with right angled triangles.
The theorem is:
[tex]a^{2} + b^{2} = c^{2}[/tex]
where:
a = length of one leg of the triangle
b = length of the other leg of the triangle
c = the length of the hypotenuse.
If triangle FGH is a right triangle then:
[tex]\sqrt{51}^ {2} + 7 ^{2} = 10^{2}[/tex]
[tex]\sqrt{51} ^{2}[/tex] is just 51
[tex]7^{2}[/tex] is 49
and [tex]10^{2}[/tex] is 100
if we add up 51 and 49 we get 100. And of course, 100 = 100,
Since the theorem works, then the FGH is a right triangle
______________________________________
Answer:
True: FGH is a right angled triangle
Jenson has a basket containing oranges, apples, and pears. He picks a piece of fruit from the basket 40 times, replacing the fruit before each draw. From these 40 trials Jenson estimates that the probability of picking an orange is 0.25, the probability of picking an apple is 0.3, and the probability of picking a pear is 0.45. How many times did Jenson pick an apple during the 40 trials?
[tex]\large\boxed{12\,\text{apples}}[/tex]
Step-by-step explanation:In this question, we're trying to find how many apples Jenson picked from the basket.
Lets gather information that can help us.
Important information:
Picked a fruit from a basket 40 timesProbability of picking an apple is 0.3With the information above, we can solve the question.
We know that he picked up a fruit 40 times, but we need to find how many apples he picked up during the 40 times.
The probability of picking an apple is 0.3, which is equivalent to 30%
This means that 30% of the 40 times he picked an apple.
We would multiply 40 by 0.3 to get our answer.
[tex]40*0.3=12[/tex]
This means that Jenson picked 12 apples.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Answer: B.12
Step-by-step explanation:
PLEASE HELP AND EXPLAIN HOW TO DO IT IM CONFUSED
[tex]3\sqrt5-2\sqrt7+\sqrt{45}-\sqrt{28}=\\3\sqrt5-2\sqrt7+\sqrt{9\cdot5}-\sqrt{4\cdot7}=\\3\sqrt5-2\sqrt7+3\sqrt{5}-2\sqrt{7}=\\6\sqrt5-4\sqrt7[/tex]
What is the volume of the composite figure with the dimensions shown in the 3 views? (Round to the nearest tenth)
Answer:
278.9 units^3 to the nearest tenth.
Step-by-step explanation:
This is a cylinder on the bottom . resting on the cylinder is a prism.
Volume of the cylinder = π r^2 h where r = 1/2 * 7 = 3.5 and h = 6.
V = π * 3.5^2 * 6 = 230.907 units^3.
Volume of the prism = l*w*h
= 4*4*3 = 48 units^3.
Volume of the composite figure = 230.907 + 48
= 278.9.
Rewrite the following linear equation in slope-intercept form.write your answer with no spaces. Y-5=3(x+1)
Answer:
[tex]y=3x+8[/tex]
Step-by-step explanation:
Slope-intercept form is as follows:
[tex]y=mx+b[/tex]
In this equation, "m" represents your slope and "b" represents your y-intercept.
To convert your equation into slope-intercept form, distribute your 3 across your parentheses and then add 5 to both sides to isolate for y.
[tex]y-5=3(x+1)\\y-5=3x+3\\y=3x+8[/tex]
A bag contains the red marbles, we orange marbles, one yellow marble, and two green marbles. Two marbles are drawn
from the bag
What is the approximate probability of choosing an orange marble and a green marble?
Save and Exit
Submit
Answer:
the answer of this question is 3/5
Answer: the answer is
0.04444
Solve x^2 - 8x = 3 by completing the square. Which is the solution set of the equation?
1st one
Step-by-step explanation:
I have answered ur question
Answer:
A
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{19}[/tex]
Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )
multiply 5x^2-6x+2 4x^2-3x
Answer:
[tex]20x^{4}-39x^{3} +26x^{2}-6x\\[/tex]
Step-by-step explanation:
Multiply the two polynomials by multiplying each term
[tex](5x^{2} -6x+2)(4x^{2} -3x)\\5x^2*4x^2+5x^2(-3x)+(-6)*4x^2+(-6x)(-3x)+2*4x^2+2(-3x)\\20x^{4}-39x^{3} +26x^{2} -6x\\[/tex]
To multiply the given expressions, use the distributive property and combine like terms. The final result is 20x⁴ - 39x³ + 26x² - 6x.
Explanation:To multiply the expression (5x²-6x+2) (4x²-3x), we can use the distributive property. Multiply the first term in the first binomial (5x²) by each term in the second binomial (4x², -3x), and then multiply the second term in the first binomial (-6x) by each term in the second binomial. Finally, multiply the third term in the first binomial (2) by each term in the second binomial. Combine like terms and simplify as needed to get the final result.
Applying this process, we get:
5x² × 4x² = 20x⁴
5x² × -3x = -15x³
-6x × 4x² = -24x³
-6x × -3x = 18x²
2 × 4x² = 8x²
2 × -3x = -6x
Combining all the terms, we have:
20x⁴ - 15x³ - 24x³ + 18x² + 8x² - 6x
Simplifying further, we get:
20x⁴ - 39x³ + 26x² - 6x
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The following list gives the number of siblings for each of 15 students.
2,2,1, 4, 4, 2, 3, 0, 0, 4, 1, 0, 4,0,2
Find the modes of this data set.
Answer:it’s the number that appears most often,so the answer would be 2,4,and 0.
Step-by-step explanation:
The modes of the data set are 0, 2, and 4
Step-by-step explanation:In this question, it is asking you to find the mode of the given data set.
We would be using the data set in the question in order to find out what the mode is.
The mode would be the number that "occurs" the most. In other words, the number(s) that are more "frequent."
Data set:
2, 2, 1, 4, 4, 2, 3, 0, 0, 4, 1, 0, 4, 0, 2
Now, we could count how many of each numbers there are.
0 = 4 (Most)
1 = 2
2 = 4 (Most)
3 = 1
4 = 4 (Most)
When you're done counting the numbers, you would notice that 0, 2, and 4 have the highest number of occurrence in the data set.
This means that the modes of the data set are 0, 2, and 4
I hope this helps you out.Good luck on your academics.Have a fantastic day!The cosine ratio is the ___ side over the hypotenuse
Which lengths would form a right triangle?
O 9, 12, and 14
O 24,7, and 26
o 21, 16, and 12
O 30, 24, and 18
Answer:
O 30, 24, and 18
Step-by-step explanation:
18^2+24^2=30^2
324+576=900
Final answer:
Using the Pythagorean theorem, only the set of lengths 24, 7, and 26 satisfy the condition for a right triangle, as 24² + 7² equals 26².
Explanation:
The question seeks to determine which set of lengths can form a right triangle. When assessing whether a given set of three lengths can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse). The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.
We will check each set of given lengths:
For lengths 9, 12, and 14: 9² + 12² = 81 + 144 = 225, which is not equal to 14² (196), so this is not a right triangle.For lengths 24, 7, and 26: 24² + 7² = 576 + 49 = 625, which is equal to 26² (625), so this set of lengths can form a right triangle.For lengths 21, 16, and 12: 21² + 16² = 441 + 256 = 697, which is not equal to 12² (144), so this is not a right triangle.For lengths 30, 24, and 18: 30² + 24² = 900 + 576 = 1476, which is not equal to 18² (324), so this is not a right triangle.Therefore, the lengths that would form a right triangle are 24, 7, and 26.
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 48°. The distance between the Gladstone and the Norman is 4590 yards. The Norman measures an angle of 55° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?
Answer:
=3501 yards.
Step-by-step explanation:
The three ships form a triangle. From the Voyager the angle between the Norman and the Gladstone=180-(55+48)=77°
Let the position of the Voyager be V that of Norman be N and that of the Gladstone be G
Then, the distance between Norman and voyager is g
g/sin G=v/ Sin V
4590/Sin 77=g/Sin 48
g=(4590 Sin 48)/Sin 77
=3500.8 yards
The distance between the Norman and the voyager= 3501 yards.
Which of the following functions best describes this graph?
A.y=x2+9x+18
B.y=x2-2x+4
C.y=(x-3)(x-6)
The correct equation for the given graph will be option A that is
y=[tex]x^{2} +9x+18[/tex]
What is an equation?
It is a relationship between two variables and having a equal to sign in between.
How to draw a graph?Firstly we need to find the points of the respective equations.
y=[tex]x^{2} +9x+18[/tex]
y=[tex]x^{2}[/tex]+6x+3x+18
y=x(x+6)+3(x+6)
y=(x+3)(x+6)
Put this equal to 0 and we get x=-3 and x=-6
y=[tex]x^{2} -2x+4[/tex]
It is a wrong equation.
y=(x-3)(x-6)
put this equal to 0 we get x=3 and x=6
Now we have to check in the graph whether points (-3,0)(-6,0) satisfies or (3,0)(6,0)
We can easily see that (-3,0)(-6,0) satisfies the graph.
Hence the correct equation is y=x2+9x+18
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Which of the following statements must be true, given that ABC= XYZ and AB = 10 cm?
Answer:
XY=10 cm
Step-by-step explanation:
The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which of the statements is true?
Answer:
the answer is D
Step-by-step explanation:
if you look on the graph and compare the statements you'll see none of them correlate except for the last one. 7 erasers cost 3.50, since the point on the graph is (7, 3.50)
Answer:
The correct option is D) Seven eraser cost $3.50
Step-by-step explanation:
Consider the provided graph.
The graph shows the relationship between the total cost and the number of erasers bought at the student store.
Here the x-axis represents the number of erasers bought and the y-axis represents the total cost.
Now consider the provided options.
Options (A) Each eraser cost $1.00
This option is incorrect because when x = 1 the value of y = 0.5, that means the cost of each eraser is $0.5
Options (B) Each eraser cost $1.50
This option is incorrect as the cost of each eraser is $0.5
Options (C) Three eraser cost $6
This option is incorrect because when x = 3 the value of y = 1.5, that means the cost of 3 eraser is $1.5
Options (D) Seven eraser cost $3.50
This option is correct because when x = 7 the value of y = 3.5, that means the cost of 7 eraser is $3.5
Which graph shows the piecewise function given below?
The graph that represents the given piecewise function is the one on the right. Therefore the correct answer is option b.
The piecewise function f(x) is defined as follows:
f(x) = -x if x ≤ 3
f(x) = 2 if x > 3
To graph this piecewise function, you would draw two separate segments:
For x values less than or equal to 3, you would graph the line y = -x, which has a negative slope and goes through the point (3, -3). This line represents the function f(x) = -x for x ≤ 3.
For x values greater than 3, you would graph the horizontal line y = 2. This line represents the function f(x) = 2 for x > 3.
The transition from the first segment to the second occurs at x = 3. At this point, you would typically draw an open circle to indicate that the function is defined separately for x ≤ 3 and x > 3.
The graph will consist of a line sloping downward to the left (y = -x) for x ≤ 3 and a horizontal line at y = 2 for x > 3.
Therefore, the correct answer is option b.
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need help asap. Consider the diagram.
Given that r||s and q is a transversal, we know that by the [________].
ANSWER
alternate interior angles theorem
EXPLANATION
According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.
From the above diagram line r is parallel to line s, therefore
[tex] \angle \: 3 \cong \angle6[/tex]
and
[tex] \angle \: 4\cong \angle5[/tex]
because they are alternate interior angles.
See attachment for how to spot alternate interior angles.
Question:
Given that r||s and q is a transversal, we know that by the [________].
Answer:
alternate interior angles theorem