Diagonals of a trapezoid intersect each other at point E, and the extensions of the legs of the trapezoid intersect each other at point F. Prove that line EF bisects the bases of the trapezoid.
PLEASE HELP, IT’S DUE TOMORROW. 50 POINTS AND BRAINLIEST.
Answers
Answer:
See Below.
Step-by-step explanation:
Let the intersection point above E be K, and let the intersection point below E be J.
Since ABCD is a trapezoid:
[tex]\displaystyle AB\parallel DC[/tex]
Therefore:
[tex]\displaystyle \angle AJF\cong \angle DKF[/tex]
And:
[tex]\displaystyle \angle DFJ\cong \angle DFJ[/tex]
So, by AA-Similarity:
[tex]\displaystyle \Delta DFK\sim \Delta AFJ[/tex]
CPSTP (Corresponding Parts of Similar Triangles are Proportional):
[tex]\displaystyle \frac{KD}{JA}=\frac{FK}{FJ}[/tex]
Likewise, do the same to the other side. Since AB is parallel to DC:
[tex]\displaystyle \angle BJF\cong CKF\text{ and } \angle CFJ\cong \angle CFJ[/tex]
Hence:
[tex]\Delta CFK\sim \Delta BFJ[/tex]
By CPSTP:
[tex]\displaystyle \frac{KC}{JB}=\frac{FK}{FJ}[/tex]
Substitution:
[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JB}[/tex]
Since AB is parallel to DC:
[tex]\displaystyle \angle CDB\cong \angle ABD[/tex]
By vertical angles:
[tex]\angle DEK\cong BEJ[/tex]
Hence, by AA-Similarity:
[tex]\Delta DKE\sim \Delta BJE[/tex]
CPSTP:
[tex]\displaystyle \frac{KD}{JB}=\frac{KE}{JE}[/tex]
Likewise:
[tex]\angle DCE\cong \angle BAC[/tex]
And by vertical angles:
[tex]\displaystyle \angle CEK\cong \angle AEJ[/tex]
Hence:
[tex]\Delta CKE\sim \Delta AJE[/tex]
CPSTP:
[tex]\displaystyle \frac{KC}{JA}=\frac{KE}{JE}[/tex]
Substitution:
[tex]\displaystyle \frac{KD}{JB}=\frac{KC}{JA}[/tex]
Now, we have obtained that:
[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JB}[/tex]
And:
[tex]\displaystyle \frac{KD}{JB}=\frac{KC}{JA}[/tex]
In the second proportion, multiply both sides by JA:
[tex]\displaystyle \frac{KD\cdot JA}{JB}=KC[/tex]
In the first equation, multiply both sides by JB:
[tex]\displaystyle \frac{KD\cdot JB}{JA}=KC[/tex]
Substitute:
[tex]\displaystyle \frac{KD\cdot JA}{JB}=\frac{KD\cdot JB}{JA}[/tex]
Cross-multiply:
[tex]JB\cdot KD\cdot JB=JA \cdot KD\cdot JA[/tex]
Cancel out KD and simplify:
[tex]JB^2=JA^2[/tex]
Therefore:
[tex]JB=JA[/tex]
And using the first proportion again:
[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JA}\Rightarrow KD=KC[/tex]
Hence, EF bisects AB and DC, the bases of the trapezoid.
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Step-by-step explanation:
see the photo
............
1.) 7+7/9x=−42 2.) 4x+1=−15 3.)−4(x−3)=−40
Answers
Answer:
1) x= -1/27
2) x=-4
3) x=13
Step-by-step explanation:
1) 7+7/9x= = -42
14/9x= = -42
14/9x X 9x= -42 X 9x
14= -378x
-378x= 14
-378x/-378= 14/-378
x= -1/27
2) 4x+1=−15
4x+1-1=-15-1
4x=-16
4x/4= -16/4
x=-4
3) −4(x−3)=−40
-4(x-3)/-4= -40/4
x-3=10
x-3+3=10+3
x=13
Plz help will be marked BRAINLIEST
Answers
Answer:
a-45
b-30
c-90
Step-by-step explanation:
blue shape-90 degree angle
pink is 45 since 2 make up a quadrant
aqua is 30 because half 2 quadrants equal 180.
180-(45x2)=90
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hope this helps!
im failing lol help The areas of the squares adjacent to two sides of a right triangle are 29.25 units^2 and 13 units ^2
Answers
Answer and Step-by-step explanation:
To find the length of z, we need the lengths of the other 2 sides first. Simply take the square root of both areas and that will be your sides.
[tex]\sqrt{13}[/tex] and [tex]\sqrt{29.25}[/tex]
Now find z, the hypotenuse.
[tex](\sqrt{13}) ^2 + (\sqrt{29.25} )^2 =z^2\\\\13 + 29.25 = z^2\\\\42.25 = z^2\\\\\sqrt{42.25} = z\\\\6.5 = z[/tex]
6.5 is the answer.
#teamtrees #PAW (Plant And Water)
Find the mean of the set of data. Use a calculator if necessary.
1, 5, 8, 10, 11
The Mean is _____.
5
7
6
8
Answers
Answer:
7
Step-by-step explanation:
mean is average of the numbers
add all values then divide by the numbers
(1+5+8+10+11) / 5
35 / 5 = 7
1+5+8+10+11 is 35
35/5 is 7
What is the domain of the function y = √2x − 6
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Fracisco's game involves 3 green, 2 yellow, 4 red, and 3 black marbles. If he randomly draws three marbles from the bag, without replacement, what is the probability that he will draw yellow, and then red, and then black?
StartFraction 1 over 192 EndFraction
StartFraction 1 over 72 EndFraction
StartFraction 3 over 220 EndFraction
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Probability of drawing a yellow is 2/12
Don’t replace the marble
The probability of drawing a red marble is 4/11
Don’t put the marbles back in
The probability of drawing a black is 3/10
Multiply them together.
2/12 times 4/11 times 3/10.
24/1320 or. 1/55
Answer:
There are 12 marble if you add them all together, (3+2+4+3=12)
the probability of drawing a yellow is 2/12 the probability of drawing a red marble is 4/11 The probability of drawing a black is 3/10Multiply them together.
2/12 times 4/11 times 3/10.
=24/1320
Step-by-step explanation:
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Enter your answer in simplified fraction form.
There are 4 queens in a standard deck of 52 cards. You pick one card at random. What is the probability of not picking a queen?
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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An ice cream sandwich has a length of 4 inches, width of 212 inches, and height of 34 inches.What is the volume of the ice cream sandwich?
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Answer:
28832
Step-by-step explanation:
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Answer:
28832
Step-by-step explanation:
Formula: L x W x L
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50, 22, 42, x, 30, 42, 9, 23
Given that the range of the numbers is 66
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Step-by-step explanation:
this may be the answer
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Answer:
i think it's D
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Step-by-step explanation:
Please give brainliest and a Heart
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Step-by-step explanation:
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Answers
Answer:
The answer is 192.78 inches
Step-by-step explanation:
An oval is formed by a rectangle with semicircles at each end. We can visualize this easily.
The length of the rectangle is 54 inches.
The width of the rectangle is 27 inches.
The perimeter of rectangle is =
=
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r =
The circumference is given by :
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Now as the described oval shape is a complete figure without lines inside, we will subtract the width of both sides of the rectangle from the complete perimeter.
The complete perimeter is = inches
The inner edge perimeter will be = = 192.78 inches
pls mark as brainliest
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Step-by-step explanation:
Please help I will make brain!!
Answers
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Answers
Answer:
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Step-by-step explanation:
Formulas we'll use: area of a rectangle is length x width, and area of a triangle = 1/2x base x height
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The explanation can be seen above:)
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Answers
Answer:
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Step-by-step explanation:
3 1/8 - 1/2
Get a common denominator
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Step-by-step explanation:
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1/2 is equal to 4/8, which has the same denominator as 3 1/8.
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Answer:
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Answer:
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Enter your answer in simplified fraction form
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Step-by-step explanation:
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Step-by-step explanation:
The area of the rectangular floor in Tamara's room is 95 5/6 square
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Answers
Answer:
11 ½ feet
Step-by-step explanation:
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which angles are supplementary to each other ? Select all that apply
Answers
Answer:
angles 3 and 1
angles 3 and 2
angles 2 and 1
which angles are complementary to each other ? select all that apply
Answers
Complementary angles, if added together, make a right angle or 90* angle
Please help asap or give explanation for brainliest
Answers
Answer:
Hi, I believe 1-0.25c is the correct answer.
Step-by-step explanation:
This is because 25% off would mean taking 25 off of a whole amount, which in this case would be one.
Hope this helps ;)
To encode a message, James first replaces each letter within the message with its
corresponding number, where A = 1, B = 2, · · · , Y = 25, and Z = 26. Next, James
multiplies each number by 3 and then subtracts 5, and continues this process a total
of n times. For example, when n = 2 the letter D is encoded to the number 16.
If James encoded a four letter message to the four numbers 367 205 853 1339, what
is the value of n that he used?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Answers
The value of n is 4. That means, the process is applied 4 times.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
To encode a message,
James first replaces each letter within the message with its corresponding number, where A = 1, B = 2, · · ·, Y = 25, and Z = 26. Next, James multiplies each number by 3 and then subtracts 5, and continues this process a total of n times.
To find the value of n:
We use process inversely.
Let m be the given number.
For example,
m = 16
The inverse process;
add 5 and then divide by 3 until we get the whole number.
So, first time
(16 + 5)/3 = 21/3 = 7,
Second time applying process,
(7+5)/3 = 4.
And the corresponding letter is D.
And the value of n is 2.
Now, m = 367
Applying process inversely,
First time,
(367 + 5) / 3 = 124
Second time,
(124+5)/3 = 43
Third time,
(43+5)/3 = 16
Fourth time,
(16+5)/3 = 7
m = 205
Applying process inversely,
First time,
(205+ 5) / 3 = 70
Second time,
(70+5)/3 = 25
Third time,
(25+5)/3 = 10
Fourth time,
(10+5)/3 = 5
m = 853
Applying process inversely,
First time,
(853+ 5) / 3 = 286
Second time,
(286+5)/3 = 97
Third time,
(97+5)/3 = 34
Fourth time,
(34+5)/3 = 13
m = 1339
Applying process inversely,
First time,
(1339+ 5) / 3 = 448
Second time,
(448+5)/3 = 151
Third time,
(151+5)/3 = 52
Fourth time,
(52+5)/3 = 19
We applied the process 4 times.
Therefore, the value of n is 4.
To learn more about the multiplication;
https://brainly.com/question/19634536
#SPJ2
Which group contains numbers that all round most closely to 0? 1/2,2/7,9/10 3/4,5/6,7/9 3/5 , 2/4,4/7 1/5 ,2/9 , 0/4
Answers
Answer:
0/4 and all the other numbers in it's group are super low, so the last group. 0/4 is 0.