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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Plz help will be marked BRAINLIEST!!!
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Step-by-step explanation:
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Step-by-step explanation:
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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:
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The area of the rectangular floor in Tamara's room is 95 5/6 square
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Answer:
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Step-by-step explanation:
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3√3 / √30
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Answer:
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Step-by-step explanation:
see the photo
............
A family went out to eat. Below is the number of corn dogs that each of the four people ate.
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Answer:
What are you asking? I know the number of corn dogs but what are we suposed to figure out?
Step-by-step explanation:
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
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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
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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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Answer:
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Step-by-step explanation:
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Answer:
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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
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The explanation can be seen above:)
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
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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]
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#teamtrees #PAW (Plant And Water)
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Probability of drawing a yellow is 2/12
Don’t replace the marble
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Don’t put the marbles back in
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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:
PLZ HELP ME ANSWER THIS NO INCORRECT PLS THANK YOU
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2. Simplify 5x−y−3x−2y to 2x−3y.
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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.
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Now, m = 367
Applying process inversely,
First time,
(367 + 5) / 3 = 124
Second time,
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Third time,
(43+5)/3 = 16
Fourth time,
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Applying process inversely,
First time,
(205+ 5) / 3 = 70
Second time,
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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,
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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
Please help I will make brain!!
Answers
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Plz help will be marked BRAINLIEST
Answers
Answer:
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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.
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Answer:
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Step-by-step explanation:
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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
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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
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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
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35 / 5 = 7
1+5+8+10+11 is 35
35/5 is 7
help plzzz...also give steps
Answers
Answer:
392π
Step-by-step explanation:
Equation is 1/3(piR^2)*h
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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.