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.
Related Questions
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)
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
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
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
StartFraction 1 over 55 EndFraction
Answers
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:
The area of the rectangular floor in Tamara's room is 95 5/6 square
feet. The width of the room is 8 1/3 feet. What is the length of Tamara's
room?
Answers
Answer:
11 ½ feet
Step-by-step explanation:
Explanation : Area = L • W, so if you do 95 5/6 divided by 8 1/3 you get 11 1/2
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
help plzzz...also give steps
Answers
Answer:
392π
Step-by-step explanation:
Equation is 1/3(piR^2)*h
Radius is 7, 7 squared is 49.
1/3(49π)(24)
392π
PLZ HELP ME ANSWER THIS NO INCORRECT PLS THANK YOU
Answers
Answer:
number 1 is A: 8<4x+10
number 2 is i: 2x+7<5
number 3 is E: 8<3x+4
number 4 is D: 2-5x<5
Please answer asap :)
Will Give Brainliest to correct answer
Answers
3√3 / √30
step by step pls
Answers
Answer:
3√10/10
Step-by-step explanation:
see the photo
............
Mark wants to paint a mural. He has 1 1/4
gallons of yellow paint, 1 1/5
gallons of green paint, and 7/8 gallon of blue paint. Mark plans to use 3/4
gallon of each paint color. How many gallons of paint will he have left after painting the mural? Enter your answer as a simplified fraction.
Mark will have gallons of paint left after painting the mural.
Answers
Answer: 1 5/24
Step-by-step explanation:
Please give brainliest and a Heart
Plz help will be marked BRAINLIEST!!!
Answers
Answer:
m=90
Step-by-step explanation:
if you only need to do one other angle then do m. it's a right angle
Answer:
i think it's D
it's hard to explain but i'm sure it's D
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?
Answers
Answer:
28832
Step-by-step explanation:
thats a big ice cream sandwich, can i have some?
Answer:
28832
Step-by-step explanation:
Formula: L x W x L
4x212x44= 28832
Help with math 10 points
Answers
2. Simplify 5x−y−3x−2y to 2x−3y.
3. Add 2y to both sides.
4. Simplify −3x−10x+14 to −13x+14.
(I answered it from top to bottom, so it would go top 1 2 to botttom 3 4)
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?
Answers
Answer:
1/13
Step-by-step explanation:
Answer:
1/13 is the answer
Step-by-step explanation:
A family went out to eat. Below is the number of corn dogs that each of the four people ate.
Answers
Answer:
What are you asking? I know the number of corn dogs but what are we suposed to figure out?
Step-by-step explanation:
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.
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
90/3=30
hope this helps!
Please help I will make brain!!
Answers
For 3 it is 12
And for 12 it is 48
Consider the following 8 numbers, where one labelled x is unknown.
50, 22, 42, x, 30, 42, 9, 23
Given that the range of the numbers is 66
work out 2 values of x
this is how the answer is suppose to be written:
Answers
Step-by-step explanation:
this may be the answer
but I am not that sure
What is the domain of the function y = √2x − 6
step by step pls
Answers
please help!!!!! find surface area of prism!!!!!!
Answers
Answer:
228cm^2
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
the base is a rectangle, 10 by 3 cm. 10 x 3 = 30cm^2
the sides are also rectangles, 13 by 3 cm. 13 x 3 = 39, but there are 2 of them, 39 x 2 = 78cm^2
The top and bottom are triangles, 1/2(10)(12) = 1/2(120) = 60, but there are 2 of them, 60 x 2 = 120cm^2
Add up the areas to get your total surface area. It's in square cm
30 + 78 + 120 = 228cm^2
The explanation can be seen above:)
which angles are complementary to each other ? select all that apply
Answers
Complementary angles, if added together, make a right angle or 90* angle
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
The probability of not picking a queen i
Answers
Answer:
1/13
Step-by-step explanation:
Answer:
1/13 is the answer
Step-by-step explanation:
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
Subtract:
3 1/8 - 1/2
Answers
Answer:
2 5/8
Step-by-step explanation:
3 1/8 - 1/2
Get a common denominator
3 1/8 - 1/2 *4/4
3 1/8 - 4/8
Borrow 1 from the 3 in the form of 8/8
2 + 8/8+1/8 - 4/8
2 9/8 - 4/4
2 5/8
Answer:
21/8 or 2 5/8
Step-by-step explanation:
Step 1: Find a common denominator for 1/2 to have the same denominator as 3 1/8:
1/2 is equal to 4/8, which has the same denominator as 3 1/8.
Step 2: Convert the mixed fraction into an improper fraction so it will be easier to subtract.
3 1/8 = 25/8
Step 3: Now subtract:
25/8 - 4/8 = 21/8 or 2 5/8 (keep the denominator the same)
Now you know that someone stole 4 pieces of your pizza :(
Hope this helps :)
-jp524
What angle is complementary to 1 ? I'll mark brainliest
Answers
Answer:
angle 2
Step-by-step explanation:
complementary angle to angle 1 is angle 2 because in complementary angle sum of two amgle is 90 degree and when we add angle 1 and angle 2 it gives us 90 degree since they are perpendicular.
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 54 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
(π = 3.14)
192.78 inches
246.78 inches
277.56 inches
331.56 inches
please help lol
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 =
=
= 162 inches
And because there are two semicircles, we can combine them to form a circle. So, perimeter of a circle is called a circumference.
The width of the rectangle forms the diameter, so its half will be the radius.
r =
The circumference is given by :
= inches
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
Answer:
1st option
Step-by-step explanation:
Stock for the Jones Corporation starts with a value of $39.63 and gains $0.30 in value per month. Stock for the Overton Company starts with a value of $24.45 and gains $0.80 in value per month. When are the two stocks nearly equal in value?
A after 3 monthsafter 3 months
B after 4 monthsafter 4 months
C after 15 monthsafter 15 months
D after 30 months
Answers
The answer is D After 30 months EZ.
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 ;)