Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!

Answers

Answer 1

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

Given That E Is The Midpoint Of AD And BC, Which Of The Following Proves That ABCD?HELP ASAP!

Related Questions

The L.C.M of two numbers is 2079 and their H.C.F. is 27. If one of the numbers is 297, then the other number is: ​

Answers

Step-by-step explanation:

2079 / 297 = 7

that is the first indication about what we need.

but 7 itself can't be the solution, because the solution needs to contain at least a factor of 27.

297 = 27×11

therefore,

2079 = 27×11×7

and the other number must now be

27×7 = 189

because due to the HCF it has to be divisible by 27, but must have another additional factor. a factor that allows it to divide 2079 without remainder, and makes it big enough to block any LCM lower than 2079.

there are only 2 other factors available in 2079 : 11 and 7.

297 has already "taken" 11, and the two numbers cannot be the same (otherwise the LCM and the HCF would be the number itself), so that leaves 7 for the other number.

hence the solution.

the other number is 189

and the other number must then be 27×7 = 189

find the percentage change of $20 to $25

Answers

Answer:

25%

Step-by-step explanation:

Percent change formula:

[tex]C = \frac{x_{2} - x_{1}}{x_1}[/tex]

x_1 = initial value

x_2 = final value

[tex]\frac{25-20}{20} = \frac{5}{20} = \frac{1}{4}[/tex]

1/4 = 0.25

25 PERCENT INCREASE

it cant be descrase

Evaluate -(2-6)(23).
O A. -8
O B. 33
O c. - 3
O D. 8

Answers

i think it’s definitely-3

-3 c

the question in the photo

Answers

Answer: b would be the answer

Step-by-step explanation:

Find the measure of

Answers

Answer:

120° , 80° , 90°

Step-by-step explanation:

The sum of the inner angles of a triangle is one hundred and eighty degrees. and as the diagram shows, The AB is equal to AC so angle ABC is equal to angle ACB so Angle A is 180°-(30°×2)=120°

you can get the second follow the above steps

and the third one is 2x+x+x=180°

so 4x=180°

so x=45°

so 2x=90°

Q.17) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 30°and angle C = ?°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = x°

angle B = 30°

angle C = ?°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = 30°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛30° + x° + 30° = 180°

⇛60° + x° = 180°

⇛x° = 180°÷60 = 180°:60

⇛x° = 180°/60

⇛x° = 3°

Now,

⇛angle A = x = 3°

⇛angle B = 30°

⇛angle C = 30°

Answer: The value of x for the given problem is 3°

Q.18) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 50°and angle C = ?°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = x°

angle B = 50°

angle C = ?°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = 50°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛ x° + 50°+50° = 180°

⇛x° + 100 = 180°

⇛x° = 180°÷100° = 180°:100°

⇛x° = 180°/100

⇛x° = 18°

Now,

⇛angle A = x = 18°

⇛angle B = 50°

⇛angle C = 50°

Answer: The value of x for the given problem is 18°

Q.19) Given info:- In ∆ABC , AB = AC and angle A = 2x°, angle B = x°, angle C = x°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = 2x°

angle B = x°

angle C = x°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = x°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛x° + 2x° + x° = 180°

⇛2x° + 2x° = 180°

⇛4x° = 180°

⇛x° = 180°÷4 = 180°:4

⇛x° = 180°/4

⇛x° = 45°

Now,

⇛angle A = 2x = 2(45) = 90°

⇛angle B = 45°

⇛angle C = 45°

Answer: The value of x for the given problem is 45°

Tom wants to spend a total of $245 on a hotel. The total cost per night at his hotel $37 the online booking company charges a one time fee of $60. a) write and equation to represent this problem $37

Answers

Answer:

60+37x=245

Step-by-step explanation

x = 5

I need help on 26 please and thank you

Answers

Answer:

your answer is 1.65 or E :)

Need help on this! Please help

Answers

Answer:

PDR= 127

Step-by-step explanation:

About 2% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400.

Answers

Answer:

200

Step-by-step explanation:

So it'll be 400 ÷ 2 = 200 , and a way to to check your way would be 200 x 2 = 400

Determine the value Y, if X is -2
Y=X-12

Answers

10 because -2 minus 12 is 10

Pls someone help me!!

Answers

Answer:

116°

Step-by-step explanation:

Interior angles in a triangle are added up to 180°.

Therefore,

(14x + 4)° + (5x - 1)° + (2x + 9 )° = 180°

Now you can solve this equation and find the value of x.

[tex](14x + 4) + (5x - 1) + (2x + 9 ) = 180[/tex]

[tex]14x+4+5x-1+2x+9=180[/tex]

[tex]14x+5x+2x+4-1+9=180[/tex]

[tex]21x+12=180[/tex]

[tex]21x=180-12[/tex]

[tex]21x=168[/tex]

[tex]\frac{21x}{21}= \frac{168}{21}[/tex]

[tex]x=8[/tex]

Now let's find the value of angle A

14x + 4

14 × 8 + 4

116°

Help pls, due in 10 mins

Answers

Answer:

B. 39

Step-by-step explanation:

134 is a supplementary angle, so 180-134=46. 46 is the bottom left interior angle of the triangle.

Next that 56 and the bottom right exterior angle are supplementary, so 180-56=124.

now we have the bottom right exterior angle, to find the interior 180-124=56.

Then we can set up the equation to find x:

56+46+2x=180

we have 180 because all triangles angle equal 180.

calculate the equation:

combine like terms, (2x)+(56+46)=180

2x+102=180

Subtract 102 from both sides,

180−102=78

2x=78

Divide both sides by 2.

78/2=39

x=39.

What is the value of x in (2/3)x=4/9?

Answers

Answer:

The value of x would be 2/3

Answer:

the answer for x is 2

Step-by-step explanation:

Can anyone help me please anyone please

Answers

Answer:

121

Step-by-step explanation:

Since the two lines are parallel, they will have the same angles, so all we need to do is find the angle that is next to 59°. Let's label this y °.

In other words, y °, the angle next to 59°, is equal to x°.

Since we are dealing with angles of a straight line, we know that the two angles of either line will add up to be 180°.

So, 59° + y ° = 180°

Isolate y by subtracting 59 from 180.

180 - 59 = 121

y ° = 121

So, x° = 121°

SALE
75% OFF
original price!
If a desk has a sale price of $13, what was the original price?

Answers

Answer:

52$

Step-by-step explanation:

13 (75% off) so 13 is 1/4 the price.

13x4 = 52

The new location for a park needs to be exactly 5 miles from the school. When plotted on the coordinate plane, the school is located at (3, 3).

Use the Pythagorean theorem to determine two possible locations on the coordinate plane for the park.

Answers

Answer:

the answer is -1, 0 and 6, -1

Step-by-step explanation:

-1, 0 and 6, -1

(Hope this helps can I pls have brainlist (crown)☺️)

what is the distance between 24 ft and 10 ft

Answers

Answer:

the distance is 14 feet. hope this helps

-3/4(x+2)=6

What is the answer please explain how u got it​

Answers

Step-by-step explanation:

1.) distribute (-3/(4x+8)=6)

2.) move 8 (-3/4x=-2)

3.) multiply by 4x (-3= -8x)

4.) divide by -8 (x=2.6)

:)

The answer is: x = -10; Step 1- Combine multiplied terms into a single fraction: -3(x+2)/4 = 6. Step 2- Distribute: -3x - 6/4 = 6. Step 3- Multiply all terms by the same value to eliminate fraction denominators: 4 x -3x - 6/4 = 6 x 4. Step 4- Cancel multiplied terms that are in the denominator: -3x - 6 = 4 x 6. Step 5- Multiply the numbers: -3x - 6 = 24. Step 6- Add 6 to both sides of the equation: -3x - 6 + 6 = 24 + 6. Step 7- Simplify: -3x = 30. Step 8- Divide both sides of the equation by the same term: -3x/-3 = 30/-3. Step 9- Simplify: x = -10.

Jane has 125 pairs of shoes if she's worn 20% of her shoes how many pairs has she worn

Answers

25 shoes because 125•.20=25

simplify (x^5-y^5) ÷(x-y) (this question is a part of polynomials chapter) please explain and tell me the answer

Answers

Answer:

Step-by-step explanation:

[tex]x^{n}-y^{n} =(x -y)(x^{n-1} + x^{n-2}*y^{1} +......+ xy^{n-2} + y^{n-1}\\\\\dfrac{x^{5}-y^{5}}{x-y}=\dfrac{(x -y)*(x^{4}+x^{3}*y^{1}+x^{2}*y^{2}+x*y^{3}+y^{4}}{(x-y)}\\\\[/tex]

            = x⁴  + x³y + x²y² + xy³ + y⁴

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?

9 feet
18 feet
30 feet
33 feet

Answers

2I + 2w = 48
9 feet is the answer.
Have a great day/night

Answer:

Step-by-step explanation:

The Width of the garden will be 9 feet.

Step-by-step explanation:

Given:

Manny has wood =48 feet

Length of the garden = 15 feet

The equation which can be used  .

We need to find the width of the garden.

Solution :

Now Length of the garden is given we will substitute in the given equation to find the width.

Now Using Subtraction property we will subtract both side by 30 we get;

Now Using Division Property we will divide both side by 2 we get;

Hence the Width of the garden will be 9 feet.

CHINESE SOCIAL CREDIT POINTS

What do you think about Mao Tse-tung

Answers

Answer:Stuff Step-by-step explanation:

If a 12-foot-tall object casts a 9-foot shadow, how long a shadow would a 4-foot-tall object cast at the same time and place

Answers

Answer:

I think it is 3 feet

Step-by-step explanation:

12:9 is equal to 4:3

4:? should also be equal to 4:3, so ?=3

Hope this helps

let me know if it does and if it is right

r^2 - 8r - 22 = 6 solve for r

Answers

Answer:

-34

Step-by-step explanation:

r^2 - 8r - 22  ( R = 6)

6^2 =36   (8r = 8*6=48)

36 - 48 =  -12

-12 - 22 = -34

An electronics store is having an 18% off sale on everything in the store. To the nearest cent, which of the following could represent regular prices and sale prices of items in the store during the sale? Select all that apply.

Answers

What do I select? You didn't put anything here.

The 18% off on the regular price of $55.43 is $45.45 so (A) is correct and the 18% off on the regular price of $29.99 is $24.59 so (B) is correct rest is not true.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The 18% off of x ⇒ x - (18/100)x = 0.82x

Therefore, 18% off of $55.43 → 0.82 × 55.43 =  $45.45

18% off of $29.99 → 0.82 × 29.99 = $24.59

18% off of $215.33→ 0.82 ×215.33 =$172.26

18% off of 849.50 → 0.82 ×849.50 = $679.60

18% off of 652.30→ 0.82 ×652.30 =  $534.89

Hence "The 18% off on the regular price of $55.43 is $45.45 and the 18% off on the regular price of $29.99 is $24.59 rest are not true.

For more about the percentage,

brainly.com/question/13450942

#SPJ5

Given question is incomplete,complete question follows ;

An electronics store is having an 18% off sale on everything in the store. To the nearest cent, which of the following could represent regular prices and sale prices of items in the store during the sale? Select all that apply.

Multiple select questions.

A)

regular price: $55.43, sale price: $45.45

B)

regular price: $29.99, sale price: $24.59

C)

regular price: $215.33, sale price: $172.26

D)

regular price: $849.50, sale price: $679.60

E)

regular price: $652.30, sale price: $534.89

solve step by step and explain
factorize
6(2a+3b)² - 8(2a + 3b)​

Answers

Answer:

Step-by-step explanation:

Find the slope and the y−intercept of the line in the graph.



The slope is .

The y−intercept is .

Can anyone help me?

Answers

Answer:

slope: 5intercept: 4

Step-by-step explanation:

It works well to find the slope using points where the graph crosses grid intersections. We see two of those are (0, 4) and (1, 9). The slope formula tells us ...

  m = (y2 -y1)/(x2 -x1)

  m = (9 -4)/(1 -0) = 5

The slope is 5.

__

The y-intercept is the value of y when x=0. The point (0, 4) tells us ...

The y-intercept is 4.

I NEED HELP please help

Answers

Answer:

1. 2/5, 2. -1. 3. 5/2, 4. 1, 5. 1/5, 6. -4/3, 7. 1/3, 8. -1/10

Step-by-step explanation:

1-3: the formula for slope is (y2 - y1)/(x2 - x1) for points (x1, y1) and (x2, y2)

1. we have points (-2, -1) and (3,1) ,plug these into the formula to get (1-(-1))/(3-(-2)) = (1+1)/(3+2) = 2/5 so the slope is 2/5

2. we have points (-3, 2) and (2, -3): (-3-2)/(2-(-3)) = -5/5 = -1

3. (-1, -2) (1,3): (3-(-2))/(1-(-1)) = 5/2

4-6: you can use the same formula

4: (1,0) (3,2): (2-0)/(3-1) = 2/2 = 1

5. (8,0) ( 13, 1) (1-0)/(13-8) = 1/5

6. (2, -1) ( 5, -5) (-5+1)/(5-2) = -4/3

7-8: slope= rise/run

7. rise=8, run=24, 8/24=1/3

8. rise=-100, run=1000, slope= -100/1000 = -1/10

i need the solution to this problem pls!

Answers

Answer:

FE = 43.2

Step-by-step explanation:

FE/36 = 24/20

multply both sides by 36

FE = 24/20 * 36

FE = 43.2

Please can I have help on this?

Answers

Answer:

9 :)

Step-by-step explanation:its 9

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