Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!
Answers
The proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
The given figure showing ΔABE ≅ ΔDCE is in the image attached below.
We know that:
E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.
E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.
∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.
This means that ΔAEB and ΔDEC have:
two pairs of congruent sides - AE ≅ ED and BE ≅ EC
one pair of congruent included side - ∠AEB ≅ ∠CED
Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.
If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.
Therefore, AB∥CD by the CPCTC Theorem.
Thus, the proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
Learn more about the CPCTC Theorem on:
https://brainly.com/question/14706064
Related Questions
Find the number that makes the ratio equivalent to 2:5.
Answers
Answer:
Answer: The fractions equivalent to 2/5 are 4/10, 6/15, 8/20, etc.
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Answers
Answer: c. x + 3
Step-by-step explanation:
The first equation tells us the total area of the cloth. The second is the area of each piece. Divide the total area by the piece area to determine how many individual pieces can be made.
(x^3 + 27) can be factored into:
(x+3)(x^2 - 3x + 9) [Not easy, but true]
[(x+3)(x^2 - 3x + 9)]/(x^2 - 3x + 9)
(x^2 - 3x + 9) is on both sides, so it cancels, leaving (x + 3)
3. George is at the craft show selling homemade ice cream. He must pay
$45 for a booth rental and costs him $3.50 to make each Ice cream
cone. He sells each ice cream cone for $5.00.
The inequality 45 + 3.50c < 5c represents the situation in which George
makes a profit
a). Will George make a profit if he sells 29 cones? Explain why or why not.
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Answer:
no 146.5 > 145
Step-by-step explanation:
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Answer:
ASWKT TAKING X AS ANY NO.
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by substituting we get answer as 2,0
Step-by-step explanation:
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Answer:
M=4 if not 1/4
Step-by-step explanation:
hope this helps sorry if it was incorrect have a great rest of the day :)❤
Karen purchased the DVD player shown in the sign on the right. Find the percent markdown rounded to the nearest percent. (SALE! Was $175.90. now $153.77)
HELP ME PLZZZ
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Answer:
probably 2.................
How do you find the positive/negative intervals of f(x) = 3/x + 5?
Answers
[] The positive interval is where the function is above the x-axis, and the negative interval is where the function is below the x-axis.
[] To find it, we can graph the function
() See attached
[] When the function is equal to less than 0, it'll be negative, otherwise it is positive
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Help please I need help
Answers
Answer:
I think it would be A??? idfk man
Use the diagram to the right for questions 16 - 20.
MNP ~ SRP
Answers
Answer:
16) 16/3
17.) ength of PM = 20/3
18.) 60
19.) 30
20.) true
Step-by-step explanation:
4/6 = x/8
32/6=x
16/3=x
4/6 = x/10
20/3 = x
I do this do y'all can get extra point and complete challenges!
What is 4 + 4
Answers
8 is the correct answer. By the way, Thank you for the few extra points.. It is very appreciated.
Which of the following is the midsegment of triangle ABC ?
Α. AL
B. LM
C. LB
D. MC
Answers
Answer:
LM
Step-by-step explanation:
Identify two opposite rays.
Answers
Answer:
B and D
Step-by-step explanation:
opposite rays 180° to each other
here B and D are opposite rays
Answer:
B and D
Step-by-step explanation:
Each opposite ray need 180 degree.
Scientific Notation
Standard Form
Write this number in standard form:
4.415 x 10-8
Answers
2÷2563783939282727262626266262534434262788900
Answers
Answer:
128189196964136363133131267217131394450
Step-by-step explanation:
hope this is helpful
Which is the better buy in each problem??
Answers
Answer:
1 - quarts of juice for 5.82 (the first one)
2 - 9.84 for a 12 pack of batteries (the second one)
3 - 24-pack of pencils for 2.64 (the first one)
4 - $2.46 for a 12-ounce jar of jam (the first one)
Step-by-step explanation:
Have a nice day
о
3. Aspect Ratios (Tires)
If you have changed the tires on your car, the original diameter is 21 inches. to a new diameter of 25.2 inches,
how fast are you actually going if your speedometer is reading 53 mph?
a
44.2 mph
b. 63.6 mph
c. 60.8 mph
d. 53 mph
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Write the equation of the line in Slope-Intercept Form given the information below. Slope =4 Point =(1,−1) slope-intercept form
Answers
Answer:
y = 4x + -1/1
-1/1 as a fraction. Down by 1 and right by 1
The equation of line in slope intercept form which is passing through
(1, -1) is y = 4x -5.
What is the slope of line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
What is the equation of line in slope intercept form?The equation of line in slope intercept form is given by y = mx + c.
According to the given question.
We have
The solpe of the line, m = 4
Also, the point through which the line is passing, [tex](x_{1} , y_{1}) = (1, -1)[/tex]
Since, we know that the equation of line in slope intercept form of the line is given by
y = mx +c
Since, the above line is passing through (1, -1) and the slope is 4.
Therefore,
-1 = 4(1) + c
⇒ -1 = 4 + c
⇒ -1 -4 = c
⇒ c = -5
Substitute the value of m and c in the equation y = mx + c.
⇒ y = mx + c
⇒ y = 4x -5
Therefore, the equation of line in slope intercept form which is passing through (1, -1) is y = 4x -5.
Find out more information about equation of line in slope intercept form here:
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In the figure, Line a is parallel to line b.
A. Which equation can be used to determine the value of x?
a
3x = 180 - 2x + 20
b
3x = 2x + 20
c
90 - 3x = 2x + 20
d
3x + 2x + 20 = 180
Answers
Answer:
b
Step-by-step explanation:
1. ) Find the mean for each data set. ROUND FINAL ANSWERS TO THE TENTHS PLACE.
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Answer:
710
Step-by-step explanation:
81+74+72+66+67+72+66+66+72+65+71= 701
701 rounded to the nearest tenth is 710
A scientist collected two sample sets of snowfall data. Which statistic should he use to compare the spread of the two sets of data? median mode mean standard deviation.
Answers
Answer:
standard deviation on edge
Step-by-step explanation:
The statistic should he use to compare the spread of the two sets of data is the standard deviation.
What is a standard deviation?The standard deviation measures how spread out the data is from the mean, and it is a measure of the average distance of the data points from the mean.
We have,
The standard deviation is the statistic that should be used to compare the spread of two sets of data.
The standard deviation measures how spread out the data is from the mean, and it is a measure of the average distance of the data points from the mean.
A larger standard deviation indicates that the data points are more spread out, while a smaller standard deviation indicates that the data points are more tightly clustered around the mean.
By comparing the standard deviations of the two sample sets of snowfall data, the scientist can determine which set has a larger or smaller spread of data.
Thus,
The statistic should he use to compare the spread of the two sets of data is the standard deviation.
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If f(x) =6(9)^x then f(1/2)=?
Answers
Answer: f(1/2) = 18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
In order to find f(1/2), we want to substitute 1/2 for x in our equation.
[tex]f(\frac{1}{2}) = 6(9)^{\frac{1}{2} }[/tex]
Then we can solve.
[tex]9^\frac{1}{2}[/tex] = 3, which means our equation is now:
[tex]f(\frac{1}{2}) = 6(3)[/tex]
6 * 3 = 18, so now we have:
[tex]f(\frac{1}{2}) = 18[/tex]
Find the constant of proportionality and write an equation for the following proportional relationship.
You drove 330 miles in 6 hours.
Use d to represent the distance you drove and t to represent the time
Answers
Answer:
NoShutterStock gives the correct value: 55 miles/hr (mph)
I'll only add that distance, d, is the product of time, t, and speed, s.
(Distance, d) = (Time, t x) (Speed, s)
d = ts
330 miles = (6 hours)*(s)
s = 330 miles/6 hours, or 55 mph
Step-by-step explanation:
The constant of proportionality and the equation for the proportional relationship are 55 miles per hour and y = 55x respectively.
What is proportionality?Two quantities are said to be in direct proportion (or directly proportional), if one is a constant multiple of the other, i.e. y is said to be directly proportional to x if y = kx where k is a constant.
Given that, find the constant of proportionality and write an equation for the following proportional relationship.
"You drove 330 miles in 6 hours."
Here, the constant of proportionality =
330/6 = 55 miles per hour
The equation for the proportional relationship =
y = 55x
Where, y is total distance and x is hour of travelling.
Hence, the constant of proportionality and the equation for the proportional relationship are 55 miles per hour and y = 55x respectively.
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evaluate -4(5-(36÷4))
Answers
Answer:
16
Step-by-step explanation:
- 4 ( 5 - ( 36 ÷ 4 ) )
= - 4 ( 5 - 9 )
= - 4 ( - 4 )
= - 4 * - 4
= 16
Emilino needs to arrange chairs for a drama club
meeting at his school. There are 30 students coming.
What
are the different ways he can arrange the chairs so that each
row has the same number of chairs?
This is the same as saying "find the factors of 30". There
are 5 different ways.
Answers
Answer:
(1 row & 30 columns) (2 rows & 15 columns) (3 rows & 10 columns) (5 rows & 6 columns) (6 rows & 5 columns)
Step-by-step explanation:
1 * 30 = 30
2 * 15 = 30
3 * 10 = 30
5 * 6 = 30
6 * 5 = 30
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Answer:
4/5 or .8
Step-by-step explanation:
Help given the graph of the function below what happens to f(x) when x is a small positive number?
Answers
Answer:
A
Step-by-step explanation:
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Side or Angle
The theater manager needs to set up 54 chairs for a show each row can be holed up to eight chairs the manager puts as many chairs in each row as possible how many rolls will the manager set up
Answers
Answer:
7 not 7 full rows though
Step-by-step explanation:
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Answers
[tex] \large \text{answer} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
' X ' has no value, v should consider x has ' 1 '
please help me woth this