Closside is 14 km north and 20 km east of Farlisle.
Use Pythagoras' theorem to calculate the direct distance between Closside and
Farlisle.
Give your answer in kilometres (km) to 1 d.p.

Answer:

x = 6, y = 2

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

-------------------

New rate is:

The value of JG = 24,

                      FJ = 7,

                     ∠EFH = 74°,

                     ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Solution:

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

                         ML = 7√2

                         ∠KNL = 90°

                          ∠MKJ = 45°

What are the properties of diagonals of a square?

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Solution:

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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The value of JG = 24 ,   FJ = 7,   ∠EFH = 74°,   ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

              ML = 7√2

                        ∠KNL = 90°

                         ∠MKJ = 45°

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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Answer:

5/1

Step-by-step explanation:

I think?

Answer: 0.20588235294 or ≈0.21

Step-by-step explanation: First, we should change the 7/10 into a fraction. (Divide numerator by the denominator) You should get .7 or 0.7. Then, when dividing, it would be 0.7 divided by 3.4 and I got 0.20588235294. I rounded it to the nearest hundredth to get ≈0.21. I hope this helped! Please, mark brainliest! (If can)

Standard deviation for 6,8,10,4 will be;

⇒ 2.58

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The data set is,

⇒ 6, 8, 10, 4

Now,

Since, The data set is,

⇒ 6, 8, 10, 4

Hence, Mean = 6 + 8 + 10 + 4 / 4

                     = 7

So, The standard deviation= √ (6 - 7)² + (8 - 7)² + (10 - 7)² + (4 - 7)² / (4 - 1)

                                        = √20/3

                                        = 2.58

Thus, Standard deviation for 6,8,10,4 will be;

⇒ 2.58

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The word problem have the following answers:

Word problems are mathematical problems which involves the use ofordinary words, instead of mathematical symbols.

From the question, if y is the balance after x weeks, this implies Johnson took out $45 multiplied by x in total including ATM fees, and their balance will be the equation;

y = $650 - $45x

After 8weeks, their balance will be;

y = $650 - $45(8)

y = $650 - $360

y = $290

After 8 weeks, Jackson will pay in ATM fees alone;

$5 × 8 = $40

Therefore, the equation y = $650 - $45x is to express their balance, y, after x weeks and $290 will be their balance after 8 weeks. While Johnson would have paid in $40 in ATM fees alone after 8 weeks.

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Answer:uu

Step-by-step explanation:

Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a liability to be verified by the auditors.

A tax placed on people or organizations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable income are typically used to calculate income taxes.

Tax rates might change depending on the taxpayer's attributes and source of income. As taxable income rises, the tax rate can also. Corporate tax, which is often assessed at a fixed rate, is the name given to the tax charged on businesses. Individual income is frequently subject to progressive taxation.

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The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet

Assume that the center of the ellipse is at the origin.

So,  The general equation for an ellipse is:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Where:

x is Horizontal distance, in feet.

y is Vertical distance, in feet.

a is Horizontal semiaxis length (half-width), in feet.

and b is Vertical semiaxis length (height), in feet.

According to the question,

x = 3 , a = 11 and b = 6

Putting all the values ,

So , the equation of ellipse will be

[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]

Putting x = 3,

[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]

Solving for y,

[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]

=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]

=> y² = 4032 / 121

=> y = √33.32

=> y = 5.77 feet

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The correct postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.

What is supplementary angles?

Two angles are said to be supplementary if their sums total 180 degrees.

Linear Pair postulate: When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

Segment Addition Postulate: According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC. This option is not correct.

Vertical Angles: When two lines intersect each other then the angles made on the opposite sides of the intersection point is known as vertical angles and they give equal measurment. This option is not correct.

Addition Postulate states: The measure of an angle formed by two angles side by side is the sum of the measures of the two angles. This option is not correct.

Hence, the correction postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.

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The volume of the box is 858 cube inches.

A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height

length of box = 13 inches

Width of box = 11 inches

height of box = 6 inches

Volume of cuboid = length x width x height

volume of cuboid = 13 x 11 x 6 which is 858 cube inches

In conclusion the volume of the box is 858 cube inches

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Distance travelled is 300 miles

The total movement of an object, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, is referred to as distance.

According to the given information

You know the equation: D = r × t.

where D represents the distance traveled, r is the train's speed, and t denotes the amount of time (in hours) required.

Train travels for 3.75 hours at 80 miles per hour

By putting the values in the above equation

D = 80 miles in 3.75 hours per hour

  = 80 × 3.75

  = 300 miles

Distance travelled is 300 miles

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Answer:

[tex]y=\frac{2}{5}x+\frac{31}{5}[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{3-5}{-2-3}=-\frac{2}{5}[/tex].

So, the equation is:

[tex]y-5=-\frac{2}{5}(x-3) \\ \\ y-5=-\frac{2}{5}x+\frac{6}{5} \\ \\ y=\frac{2}{5}x+\frac{31}{5}[/tex]

From the statement, Anthony is correct because 3*6=18

We should know that the problem is to determine the number of pencils he bought

The given parameters are that

You can draw a 3 packages of pencils with 6 pencils in each to represent t package.

Now let us do the following:

For Neville

3*6 = 18

And also,

18÷3 = 6

For Anthony

6*3 =18 and

18÷6 = 3

In conclusion, looking at the two analysis, it seems that Anthony is more correct knowing fully well that each of the multiplications and divisions give us 18 or 6

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Complete question:

Critique Reasoning Neville and Anthony are solving this problem: Barbara bought You can draw a 3 packages of pencils with 6 pencils in each to represent t package. How many pencils did she buy in all? Neville says, “I add because of the words in all. The answer is  9 pencils.” Anthony says, “I multiply because there are equal groups. The answer is  18 pencils.” Who is correct? Explain.

Answer:

71 mph

Step-by-step explanation:

Lets call the speed of the eastbound train E and the speed of the westbound train W.

E = W - 18

distance travelled  = speed * time

thus

Wt + Et = 320

Wt + (W - 18)t = 320

factor out t

t * (2W - 18) = 320

t = 2 hours

2 * (2W - 18) = 320

2W - 18 = 160

2W = 178

W = 89

Then, E = (89) - 18 = 71 mph

Answer:

I think like this but I not sure what format you learn

By Factorise the equations we get 2 points for each equation:

for a) we get (x+4),(x-1)

for b) we get (x-3),(x+1)

for c) we get (x+4),(x-2)

a) x^2 + 3x-4

for this equation we have to take factors of -4:

x^2+4x-x-4

Taking common in the equation we get:

x(x+4)-1(x-4)

After taking common, Now we get two points:(x+4,)(x-1)

b) x^2 +-2x-3

for this equation we have to take factors of -3:

x^2-3x+x-3

Taking common in the equation we get:

x(x-3)+1(x-3)

After taking common, Now we get two points:(x-3,)(x+1)

c) x^2 + 2x-8

for this equation we have to take factors of -8:

x^2+4x-2x-8

Taking common in the equation we get:

x(x+4)-2(x+4)

After taking common, Now we get two points:(x+4,)(x-2)

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"The correct question is":

Factorise the following:

a) x ^2+ 3x-4

b) x^2 - 2x - 3

c) x ^2+ 2x - 8

The value of the expression 15/r -1 when r = 5 will be equal to 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 15/r -1. The value of r is 5. The value of the expression at r=5 will be calculated as,

E = 15/r - 1

E = 15 / 5- 1

E = 3 - 1

E = 2

Therefore, the value of the expression 15/r -1 when r = 5 will be equal to 2.

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It is to be noted that the volume of Emma's storage tank is: 785.3cubic feet.

Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.

Where:

π = 22/7

r = radius of the circular base

Recall that for Emma’s cylindrical storage tank, the radius of the base is 5 feet.

So we replace this value in the formula and calculate the area of the base, which is equal to:

A = π*5²

A = 22/7 * 5²

= 78.5714285714

[tex]\approx[/tex] 78.54 square feet.

Now we need to compute the volume of the cylindrical storage tank. The volume of a cylinder is calculated by:

V = π*r²*h,

where r is the radius of the circle and h is the height of the cylinder.

Recall that for Emma’s tank, the height is 10 feet. Hence,

We substitute these values in the formula and calculate the volume, which is equal to:

V = π*5²*10 = 785.4 cubic feet.

Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.

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Answer: 61.75

Step-by-step explanation:

Answer:

If Ana started at 7:20, ended at 7:38, and she washes 6 dishes per minute, than she has 108 dishes left to wash.

Step-by-step explanation:

Answer:

Step-by-step explanation:Answer: 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.

Step-by-step explanation:

Since we have given that

She washed 30 plates from 7:30 to 7:35,

That means in 5 minutes, the number of plates get washed here = 30

We need to find the number of plates from 7:15 to 7:38

First, we count the number of minutes

In 1 minute, the number of plates gets washed by her is given by

In 23 minutes, the number of plates gets washed by her is given by

The equation to represent how many plates Ana has left to wash at a particular time after her start at 7:15  is given by

Hence, 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.

please mark me brainlieset and click the stars i spent so long on this :>

Answer:

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

Step-by-step explanation:

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,

the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem.

If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.

ZW clearly = 3,

thus

[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],

and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.

Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],

and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that

ZX = 3√2, XY =√10, and YZ = 4

⇒ Perimeter of ΔXYZ = ZX + XY + YZ

⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4

⇒ Perimeter of ΔXYZ = 14√5 units.

To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

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Answer:

Step-by-step explanation:

The number of boxes of pies that the Chess Club must sell to reach their goal of $150 can be represented by the variable x. We can create the following equation to represent this relationship:

1.25x + 16.25 = 150

To find the number of boxes of pies that the Chess Club must sell, we can solve this equation by subtracting 16.25 from both sides and then dividing both sides by 1.25:

1.25x = 150 - 16.25

1.25x = 133.75

x = 133.75 / 1.25

x = 107.

Therefore, the Chess Club must sell 107 more boxes of pies to reach their goal of $150.

Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.

Step-by-step explanation:

The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).

the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05

The p-value of a test statistic is a measure of the probability of obtaining a result that is at least as extreme as the one observed, given that the null hypothesis is true. In other words, it is a measure of the strength of the evidence against the null hypothesis.

If the p-value of a test statistic is 0.08, it means that there is an 8% chance of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. This does not necessarily mean that the result is statistically significant at any particular significance level.

To determine whether a result is statistically significant, you need to compare the p-value to a predetermined significance level, also known as the alpha level. The alpha level is the probability of rejecting the null hypothesis when it is actually true (also known as a type I error).

If the p-value is less than the alpha level, then the result is considered statistically significant. For example, if the alpha level is set at 0.05, and the p-value of the test statistic is 0.03, then the result would be considered statistically significant.

In the case of the options you provided, the significance level that gives you the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05.

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The simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].

What is simplifying an expression?

To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.

Consider, the given expression,

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5[/tex]

To simplify this using the exponent rule:

[tex]((a)^b)^c = a^b^.^c[/tex]

⇒

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^(^-^4^*^-^3)(\frac{4}{9})^-^5\\ ((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^1^2(\frac{4}{9} )^-^5[/tex]

Now use the exponent rule:

[tex]a^ba^c = a^(^b^+^c^)[/tex]

⇒

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^(^1^2^-^5^)\\((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex]

Hence, the simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].

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As we can solve the square root 80 or [tex]\sqrt{80\\}[/tex] = [tex]\sqrt{2^4}.\sqrt{5}[/tex]

so [tex]\sqrt{2^4}.\sqrt{5}[/tex] is the correct answer for square root 80

What is Square root?

The component of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 32 or 3 3. We refer to this as a square since there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed. For instance, when n is a positive integer, n = n1/2

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolised by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.

1)

[tex]\sqrt[4]{2} .\sqrt{5}[/tex] =[tex]2^{\frac{1}{4} } .\sqrt{5}[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

2)

[tex]\sqrt{2^4}.\sqrt{5}[/tex] = [tex]2^{4.\frac{1}{2} } .\sqrt{5}[/tex]

=[tex]4\sqrt{5}[/tex] or[tex]\sqrt{16 * 5} =\sqrt{80}[/tex]

3)

[tex]\sqrt{2}. \sqrt{2}. \sqrt{5} =2\sqrt{5}[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

4)

[tex]\sqrt{2^{2} } .\sqrt{2^{2} } .\sqrt{5^{2} } = 2.2.5 \\\\\4.5 = 20[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

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ΔBAD is congruent to ΔBCD by the ASA rule.

What is the ASA congruency of triangles?

If any two angles and sides included between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle, then the two triangles are said to be congruent by the ASA rule.

In the given figure ABCD is a square.

In ΔBAD and ΔBCD

∠B ≅ ∠B ----Common Angle

∠A ≅ ∠A  ------Each of 90° angle

Side BD ≅ Side BD ----Common Side

So we can say that ΔBAD ≅ ΔBCD -----(ASA rule)

Hence, ΔBAD is congruent to ΔBCD by the ASA rule.

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