1. ABCD is a quadrilateral in which angle A = angle C and angle B = angle D
Prove that, if the opposite angles of a quadrilateral are equal, then the quadrilateral is a
parallelogram.

1. ABCD Is A Quadrilateral In Which Angle A = Angle C And Angle B = Angle DProve That, If The Opposite

Answers

Answer 1

Answer:

Quadrilateral ABCD is a parallelogram, quadrilateral with opposite sides parallel

Step-by-step explanation:

Statement,                                       Reason

∠A = ∠C,                                          Given

∠B = ∠D,                                          Given

Therefore, we have

∠A + ∠B + ∠C + ∠D = 360°,            Sum of interior angles of a quadrilateral

2×∠A + 2×∠B = 360°,                         Substitution property of equality

∴ ∠A + ∠B = 360°/2 = 180°

∠A + ∠B, are supplementary  angles,   Angles that sum up to 180°

Similarly,

∠C + ∠D, are supplementary  angles,   Angles that sum up to 180°

Therefore, segment DA is parallel to segment BC, (Lines with supplementary angles on the same side of the transversal)

Similarly, given ∠A = ∠C and ∠B = ∠D, we have;

∠A + ∠D and ∠C + ∠B are supplementary  angles,   Angles that sum up to 180°

Therefore, segment AB is parallel to segment DC, (Lines with supplementary angles on the same side of the transversal)

Therefore;

Quadrilateral ABCD is a parallelogram, quadrilateral with parallel opposite sides.


Related Questions

PLEASE help me with this question! No nonsense answers please. This is really urgent.

Answers

Answer:

A) 15.6 ft²

Step-by-step explanation:

Area of the circle

A=[tex]\pi[/tex]r²

A=[tex]\pi[/tex](5.7)²

A=102.07

Area of the segment

102.07*55/360

15.594

-56 divided by -8 find the quotient

Answers

Answer:

7

Step-by-step explanation:

We can see that we have a negative number divided by a negative number, so the negatives cancel each other out.

[tex]56\div8[/tex]

We know that 8 will go into 56 7 times, so [tex]-56\div-8=7[/tex].

Hope this helped!

Answer:

7

Step-by-step explanation:

You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?

Answers

interesting puzzle,

total CDs=[tex]39[/tex]

country CDs $c$ is half of rock CDs $r$, $r=2c$

and one fourth of soundtrack $s$ as country CDs , $c=4s$

express in common variable s, $r+c+s=39$

$2(4s)+4s+s=39 \implies s=3$

so $c=12$ and $r=24$

after borrowing 3 rock CDs, there be $21$ rock CDs rest will be same

Line a and t are parallel. What is the value of x?
7x - 48
5x
pls help me

Answers

Answer:

x = 24

Step-by-step explanation:

We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.

Then, we set the expressions equal to each other:

7x - 48 = 5x

Subtract 5x from both sides:

7x - 5x - 48 = 0

2x - 48 = 0

Add 48 to both sides:

2x = 48

Divide by 2:

x = 48/2 = 24

Thus, x = 24.

~ an aesthetics lover

choose the function where the graph is given below

Answers

Answer:

B

Step-by-step explanation:

You could've graphed your choices and find which one is a perfect match.

kelly used 2.1 x 10^6 KB of data so far this month. her younger brother joseph used 7 x 10^5 KB of the data so far this month if their share family plan allows them to use 3,000,000 KB of the data each month, how much data usage o they have available for the remainder of this month?

Answers

Answer:

They will 200,000 kb left

Step-by-step explanation:

  2.1 x 10^6=2,100,000     7 x 10^5=700,000

4. Alejandro Juarez is paid $829 every two weeks. a. What is Alejandro's yearly salary?
b. How much would Alejandro earn in one month?

Answers

Answer:

1.  21,554 PER YEAR

2. 1658 PER MONTH

Step-by-step explanation:

a.  

so there are approximately 52 weeks per year

and alejandro juarez gets 829$ per 2 weeks

1..............LETS FIGURE OUT HOW MUCH HE EARNS PER WEEK

SO 829/2=414.5

so he gets 414.5 $ PER WEEK

2............LETS MULTIPLY THE AMOUNT OF MONEY PER WEEK BY THE WEEKS

SO 414.5*52=21554

SO ALEJANDRO JUAREZ EARNS 21,554$ PER YEAR

B.

SO WE ALREDY KNOWS ALEJANDRO EARNS 414.5$ PER WEEK

AND THERE ARE APPROXIMATELY 4 WEEKS IN A MONTH

SO 414.5*4=1658

SO HE EARNS 1658$ PER MONTH

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

       ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                      PEACE!

PLEASE help me with this question! No nonsense answers please. This is really urgent.

Answers

Answer:

last option

Step-by-step explanation:

Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷  x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.

If r = 8 units and h = 5 units, what is the volume of the cylinder shown above? Use 3.14 for . A. 1,607.68 cubic units B. 653.12 cubic units C. 1,004.8 cubic units D. 452.16 cubic units

Answers

Answer:

C. 1,004.8 cubic units

Step-by-step explanation:

[tex]V = ?\\r = 8\\h =5 \\\pi = 3.14\\\\V = \pi r^2 h\\\\V = 3.14 \times 8^2 \times 5\\V = 1004.8 cubic units[/tex]

Answer:

C. 1004.8  cubic units

Step-by-step explanation:

Lets analyze the problem given, we have to find the volume of cylinder and use 3.14 as pi.

We can use the formula V=(3.14)r^2h to find the volume of the cylinder.

Below is the work to solve the formula:

8^2= 64

64(5)=320

320(3.14)=

1004.8  cubic units is our answer.

A sum of $46875 was lent out at simple interest and at the end of 1 yr 8 month, the total amount was $50000. Find the rate interest per year.​

Answers

Answer:

4%

Step-by-step explanation:

As indicated in the question, this is a simple interest question.

The formula for Simple Interest =

I = Principal × Rate × Time

In the above question, we were given the following values.

A = Total value / amount of money = $50000

Principal = $46875

Rate = ??

Time = 1 yr and 8 months

= 1 year +(8/12)

Time = 1.6666666667 years

We are asked to solve for the rate interest per year. Hence, the formula to use to solve this question is given as:

r = (1/t)(A/P - 1)

r = (1/1.6666666667)(50000/46875 - 1)

r = 0.04

Converting to percentage, rate = 0.04 × 100 = 4%

Therefore, the rate interest per year is 4%

Joan weighs 10 pounds less than her older sister. The average of the two sisters’ weights is 85 pounds. How much does Joan’s older sister weigh?

Answers

Answer:

Joan's older sister weighs 90 pounds

Step-by-step explanation:

x = older sister

x - 10 = Joan

(x + (x-10))/2 = 85

2x - 10 = 170

2x = 180

x = 90

Answer:

90 pounds

Step-by-step explanation:

We can set up an equation to find their weights.

Let's start by naming Joan's weight x.

Her sister's weight would then be x+10, since Joan weighs 10 pounds less.

To find the average between 2 numbers, you need to add them together, then divide by 2.

So we can set up the following equation:

(x+x+10)/2=85

Now let's isolate x.

We can first multiply both sides by 2.

x+x+10=170

Combine like terms.

2x+10=170

Subtract 10 from both sides.

2x=160

Subtract both sides by 2.

x=80

Joan weighs 80 pounds.

x+10 is her sister's weight.

80+10=90

Joan's older sister weighs 90 pounds.


Describe the relationship between GF and CD when the two lines are perpendicular to AB. Also describe the relationship between GF and CD is not perpendicular to AB

Answers

IF GF and CD are perpendicular to AB, one can say that they will or do not intersect each other. But if CD is not perpendicular to AB, GF and CD, do intersect at one (single) point.

What is the relationship about?

In the congruent relationship above, one can say that  two lines intersect to create a linear pair of congruent angles, and thus one can say that the lines are perpendicular in nature.

Therefore, in the case above, IF GF and CD are perpendicular to AB, one can say that they will or do not intersect each other. But if CD is not perpendicular to AB, GF and CD, do intersect at one (single) point.

Learn more about perpendicular lines from

https://brainly.com/question/379998

#SPJ1

On a time limit answer asap pls

Answers

Answer:

160°

Step-by-step explanation:

Take notice that m∠1 and m∠2 are supplementary angles, meaning their angle measures will add up to 180°.

Since we know m∠2, we can find m∠1 easily.

180-20=160°

Hope this helped!

What is the difference between {2,3} and {{2,3}}

Answers

[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3

[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]

Plz help me this is probably easy but im just not seeing it plz help me ASAP

Answers

Answer: is attatched to the photo I sent

Step-by-step explanation:

I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"

The example I'm thinking of attached too, but these over lap so its diffucult

URGENT PLZ HELP THANK YOU!

Answers

Answer:

[tex](-5)^{11}[/tex]

Step-by-step explanation:

We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].

b is 5, c is -6, and a is -5 so:

[tex]-5^{5-(-6)}\\-5^{11}[/tex]

Hope this helped!

List the following elements in proper set notation. Place the elements in numerical order within the set. 0, 1, 123, 4, 34

Answers

Answer:

{0, 1, 4, 34, 123}

Step-by-step explanation:

{0, 1, 4, 34, 123}

If it takes B hours to walk a certain distance at the rate of 3 miles per hour, the number of hours it takes to return the same distance at 4 miles per hour is...? Will mark brainlist

Answers

Answer:

It will take 0.75B hours for the return leg

Step-by-step explanation:

Here, given that the first leg of the trip was for B hours at 3 miles per hour , we want to calculate the number of hours the return leg will take at 4 miles per hour given that it is the same distance.

Mathematically, we know that ;

Distance = speed * time

So the distance taken on the first leg of the trip would be;

Distance = 3 miles per hour * B hours = 3B miles

Now, this distance was traveled on the return leg also.

This means that the time taken here will be;

Time on return leg = distance/speed = 3B/4 = 0.75B hours

find whether the following mathematical sentence are constant or variable . 'm' represent the whole numbers between 5 and 7​

Answers

Answer:

Constant

Step-by-step explanation:

Whole numbers are numbers like 1,2,3 and 4.

1.1,2.3 and Pi arent't whole numbers. Fractions like 3/4 and 5/3 aren't whole numbers.

The whole numbers starting from 5 to 7 are:

● 5, 6 and 7

You can see that we have only one whole number between 5 and 7 wich is 6.

So m has only one value (m=6).

=> m is a constant

56:31
Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?

Answers

Answer:

The equation is (2+x) / 4 = 3

Total amount of chopped vegetables = 10 pounds

Step-by-step explanation:

Meat=2 pounds

Vegetables=x

Mixture= 2+x

She divides the mixture into 4 equal portions

(2+x)/4

Each portion weighs 3 pounds

(2+x)/4=3

Solve the equation

(2+x)/4=3

Cross product

(2+x) = 4 × 3

2+x=12

x=12-2

=10

x=10 pounds

Total amount of chopped vegetables = 10 pounds

Point E is on line segment DF. Given DE
EF.
6 and DF =9, determine the length EF

Answers

Answer:

3

Step-by-step explanation:

IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.

Given parameter

DE = 6

DF = 9

Required

EF

Substituting the given parameter into the expression above to get the required will be;

DE+EF = DF.

EF = DF-DE

EF = 9-6

EF = 3

Hence the length of EF is equivalent to 3

Which equation has a constant of proportionality equal to 3? A. y= 8/5 x B. y= 1/3 x C. y= 1/4 x D. y= 18/6 x PLEASE HELP ME :c

Answers

Answer:

(D) [tex]y=\frac{18}{6}x[/tex]

Step-by-step explanation:

We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.

[tex]\frac{8}{5} =1.6[/tex] so no for A.

[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.

[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.

[tex]\frac{18}{6} = 3[/tex], so D works.

Hope this helped!

A table costs Rs 720 to make. He sells it for Rs 920. What percentage of profit did he earn?

Answers

Answer:

27 7/9%

Step-by-step explanation:

Take the selling price and subtract the cost

920 -720 = 200

Divide it by the cost

200/720

.27777777

Change to percent form

27.777777%

27 7/9%

Answer:

profit percentage = 27.8 %

Step-by-step explanation:

To find the percentage of profit we use the formula

[tex] \frac{profit}{cost \: \: price \: } \times 100[/tex]

Subtract the cost price from the selling price to obtain the profit

Cost price = Rs 720

Selling price = Rs 920

Profit = Rs 920 - Rs 720 = Rs 200

So the profit percentage is

[tex] \frac{200}{720} \times 100[/tex]

We have the final answer as

profit percentage = 27.8 %

Hope this helps you

Will Give Brainliest, Answer ASAP m∠O =
m∠N =

Answers

Answer:

∠ O = 61°, ∠ N = 119°

Step-by-step explanation:

In a parallelogram

Consecutive angles are supplementary

Opposite angles are congruent, thus

x + 2x - 3 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61°

Thus

∠ O = ∠ M = x = 61°

∠ N = ∠ P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119°

What’s is the greatest common factor of 100x^2 - 250xy + 75x

Answers

Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

Evaluate f(x) = 2|x – 5| for f(–5) and f(0).

Question 20 options:

f(–5) = –20, f(0) = –2

f(–5) = 20, f(0) = 10

f(–5) = 10, f(0) = 0

f(–5) = 12, f(0) = 5

Answers

Answer:

[tex]\Large \boxed{\mathrm{f(-5) = 20, \ f(0) = 10}}[/tex]

Step-by-step explanation:

The function is given:

f(x) = 2|x - 5|

Solve for f(-5).

x = -5

f(-5) = 2|-5 - 5|

f(-5) = 2|-10|

f(-5) = 2(10) = 20

Solve for f(0).

x = 0

f(-5) = 2|0 - 5|

f(-5) = 2|-5|

f(-5) = 2(5) = 10

A piece of aluminum occupies a volume of 13.0 milliliters and weighs 52.9 grams. What is its density of the aluminum rounded to the nearest hundredth?

Answers

The density would have to be 13

If 3sinA+4cosA=5 then find the value of cosA

Answers

Answer:

Cos A =1.4

Step-by-step explanation:

3sinA=5-4cosA; square both sides: 9sin^2(A)=25-40cosA+16cos^2(A);

9-9cos^2(A)=25-40cosA+16cos^2(A); 25cos^2(A)-40cosA+16=0=(5cosA-4)^2.

cosA=4/5 so sinA=3/5 (√(1-16/25) and sinA+cosA=7/5=1.4.

A researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18 ounce boxes is less than 18 ounces. He uses the following hypotheses: H 0: μ = 18 vs H A: μ < 18 and finds a P-value of 0.01. Draw a conclusion about the cereal box weight at a significance level of 0.05.

Answers

Answer:

We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Step-by-step explanation:

We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Let [tex]\mu[/tex] = mean weight of cereal in its 18-ounce boxes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 18       {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 18      {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}

Also, it is given that the P-value is 0.01 and the level of significance is 0.05.

The decision rule based on the P-value is given by;

If the P-value of our test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.If the P-value of our test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.

Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.

Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Arc length practice

Answers

Answer:

[tex]\large\boxed{s = 4\pi}[/tex]

Step-by-step explanation:

The arc length is determined by the formula [tex]s=r\theta[/tex], where s is the arc length, r is the radius, and [tex]\theta[/tex] is the value of the central angle (in radian formatting).

By substituting the values for the radius and the central angle, you can solve for the arc length.

[tex]\text{The radius is half of the diameter -} \: \boxed{\frac{4}{2}=2}[/tex].

The central angle is converted to radian form by multiplying the angle in degrees by the fraction of π/180 - 360° * π/180 = 360π/180 = 2π.

Now, substitute the values and solve for s.

s = (2)(2π)

[tex]\large\boxed{s = 4\pi}[/tex]

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