Given: overline LM cong overline ON and overline LO cong overline MN Prove : LMNO is a parallelogram

Answers

Answer 1

[tex]\overline {LM} \parallel \overline {ON} \ and \ \overline {LO} \parallel \overline {MN}[/tex] because they form congruent alternate interior angles with a common transversal, therefore, LMNO is a parallelogram because the opposite sides are parallel

The reason the above statement are correct is presented as follows:

The given parameters are;

[tex]\overline {LM}[/tex] is congruent to [tex]\overline {ON}[/tex] and [tex]\overline {LO}[/tex] is congruent to [tex]\overline {MN}[/tex]

Required:

To prove that LMNO (quadrilateral) is a parallelogram

Solution:

The two column proof is presented as follows;

Statement [tex]{}[/tex]           Reason

[tex]\overline {LM} \cong \overline {ON}[/tex]  [tex]{}[/tex]           Given

[tex]\overline {LM} = \overline {ON}[/tex]  [tex]{}[/tex]           Definition of congruency

[tex]\overline {LO}[/tex] ≅ [tex]\overline {MN}[/tex] [tex]{}[/tex]            Given

[tex]\overline {LO}[/tex] = [tex]\overline {MN}[/tex] [tex]{}[/tex]             Definition of congruency

[tex]\overline{LN}[/tex] ≅

[tex]\overline{LN}[/tex] =

ΔLNO ≅ ΔLMN [tex]{}[/tex]    Side Side Side (SSS) congruency postulate

∠NLM ≅ ∠LNO [tex]{}[/tex]    Cong. Parts of Cong. Triangles are Cong. CPCTC

∠NLM and ∠LNO are alternate interior angles

[tex]\mathbf{\overline {LM} \parallel \overline {ON}}[/tex]   [tex]{}[/tex]    Alternate interior angles between parallel lines are congruent

∠MNL ≅ ∠NLO [tex]{}[/tex]    CPCTC

∠MNL and ∠NLO are alternate interior angles

[tex]\mathbf{\overline {LO} \parallel \overline {MN}}[/tex]  [tex]{}[/tex]     Alternate interior angles formed between parallel lines are congruent

LMNO is a parallelogram because the opposite sides, [tex]\overline {LM} \parallel \overline {ON}[/tex] and [tex]\overline {LO} \parallel \overline {MN}[/tex] are parallel

Learn more about parallelogram here:

https://brainly.com/question/14708246

Given: Overline LM Cong Overline ON And Overline LO Cong Overline MN Prove : LMNO Is A Parallelogram
Answer 2

LMNO is a plane shape which has the properties of a parallelogram. The the explanations below, it has been proven to be a parallelogram.

A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.

To prove that LMNO as given in the question is a parallelogram:

The opposite sides of a parallelogram are congruent.

Thus,

/LM/ ≅ /ON/ (opposite side property)

/LO/ ≅ /MN/ (opposite side property)

The opposite sides are parallel to each other.

        i.e LM || ON and LO || MN

Consecutive angles are supplementary.

        i.e <MLO + <LMN = [tex]180^{o}[/tex]

also    

<LON + <MNO = [tex]180^{o}[/tex]

The diagonals are at right angles to each other.

LN ⊥ MO

Opposite angles are congruent.

     <LMN ≅ <LON  and <MLO ≅ <MNO

Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.

For more clarifications, visit: https://brainly.com/question/10988285


Related Questions

what is the domain of the function in the graph?

Answers

Answer:

6AJNSDJN

Step-by-step explanation:

Evaluate the following expression 2x - |4 - 7x| when x = -3

Answers

Answer:

-31  

Step-by-step explanation:

2x - abs(4 - 7x)

2x = 2 * - 3 = - 6

4 - 7x = 4 - 7*-3 = 4 + 21 = 25

-6 - abs(25)

-6 - 25 = -31

You should note three things.

1. the absolute value of 25 is 25

2. There is a - sign outside the influence of the 25 so 25 becomes - 25

3. - 6 - 25 = - 31

Can someone help me on this math question its confusing ill give brainly when right!!!

Answers

[tex]\huge\mathsf\green{ANSWER}:—[/tex]

The coefficients are:-

-4,-6

hope it would be helpful for you

Answer:

-4,-6

Step-by-step explanation:

coefficient is an integer that is multiplied with the variable of a single term or the terms of a polynomial

If ABCD is dilated by a factor of }, the
coordinate of B' would be:
5
С
4
3
B
2
1
-5
4 3
-2
-10
1
2
3
4
5
-1
A
B' = ([?], [ ]
D
-3
Enter

Answers

Answer:

If ABCD is If ABCD is dilated by a factor of }, the

coordinate of B' would be:2

*NEED AN ANSWER ASAP* My book didn’t explain how to solve these ones.

Answers

Answer:

1-2. AC = 13.6

BC = 8.9

3-4. A triangle such as the given value isn't possible

21in. = _____ft. terminating or repeating

Answers

Answer:

Terminating

Step-by-step explanation:

We know that 12 inches is 1 foot. We can divide to find how many feet we have.

21 / 12 = 1.75

Since the decimal ends at 0.05, the decimal is terminating.

Best of Luck!

21in.=1.75ft. terminating or repeating

Na
C
9
Which rule describes the transformation?
Parallelogram ABCD is rotated to create image
A'B'C'D'.
SEE
0 (x, y) - (y, -x)
O (x, y) + (-y, x)
O (x, y) + (-X, -y)
(x, y) - (x,-y)
5
VX
4
R
D
2
1
C
-5.-5.4.-3.-2.-
23
4
SIB
Х
2
D
A
C
B
no

Answers

Answer:

(x, y) → (y, -x)

Step-by-step explanation:

The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)

The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)

The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;

(x, y) → (y, -x)

The resulting transformation used will be (x, y) -> (y, -x)

Transformation of coordinates

Transformation are rules applied to an object to change its orientation

For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage

The coordinate of A is (2, 5) while that of A' is (5, -2).

From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.

Hence the resulting transformation used will be (x, y) -> (y, -x)

Learn more on transformation here:  https://brainly.com/question/17311824

Find the value of x. Round to the nearest tenth

Answers

Step-by-step explanation:

use cos since we're given the adjacent and asked to find the hypothenus.

cos 33° = 6/x

cross multiply

xcos33° = 6

divide both sides by cos 33°

(cos 33 is approximately 0.8387)

then x = 7.15

Answer:

[tex]x \approx 7.2[/tex]

Step-by-step explanation:

The given triangle is a right triangle this is indicated by the box around one of its angles, signifying that the angle is a right angle. One of the properties of a right triangle is the right angle trigonometric ratios. these are a series of ratios that relate the sides and angles of a right triangle. Such ratios are as follows:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Please note that the sides named ([tex]opposite[/tex]) and ([tex]adjacent[/tex]) Are subjective and change based on the angle by which one refers to. However the side ([tex]hypotenuse[/tex]) indicates the side opposite the right angle, this side does not change its name.

In this case, one is given a (33) degree angle, and the measure of the side adjacent to is, (6). One is asked to find the measure of the hypotenuse (x). It would be most logical to use the ratio of cosine (cos). Substitute the given values in and solve for (x).

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(33)=\frac{6}{hypotenuse}[/tex]

Inverse operations,

[tex]cos(33)=\frac{6}{hypotenuse}[/tex]

[tex]hypotenuse=\frac{6}{cos(33)}[/tex]

[tex]hypotenuse \approx 7.15[/tex]

Which table represents a function?

Answers

Answer:

The last one

Step-by-step explanation:

All the other tables have repeating x values

I hope this helps!

pls ❤ and give brainliest pls

− 96 ÷ −6 ÷ 8 =
a) 2 b) -2

Answers

the answer is 2………………

Answer:

answer is 2

Step-by-step explanation:

answer is 2…………………………………

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The amount of lemonade left in a pitcher would be considered ________ data.
A. neither continuous nor discrete
B. discrete
C. continuous
D. both continuous and discrete

Answers

The answer is C, both continuous

3.
In each box there are 22 eggs. How many eggs do I have if I have 12 boxes?

Answers

Number of eggs = 12x22 =264

Last week, Gina's art teacher mixed 9 pints of red paint with 6 pints of white
paint to make pink. Gina mixed 4 pints of red paint with 3 pints of white
paint to make pink.
Yesterday, Gina again mixed red and white paint and made the same
amount of paint, but she used one more pint of red paint than she
used last week. Predict how the new paint color will compare to the
paint she mixed last week.

Answers

Answer:

Step-by-step explanation:

First mix: 4 pints red and 3 pints white = 7 pints in 4:3 ratio.

Second mix: 5 pints red and 2 pints white = 7 pints in 5:2 ratio

Second music is redder than first mix.

Copy and complete the table.

Answers

Answer:

See pic below.

Step-by-step explanation:

Six pairs of shoes cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks cost as much as one pair of jeans. How many coats could I exchange for 64 pairs of socks?

Answers

Answer:

4 coats

Step-by-step explanation:

Let the cost of a pair of shoe be x.

Thus, 6 pairs would cost; 6x

Thus,1 coat will cost 6x.

2 pairs of jeans cost as much as 3 pairs of shoes.

Thus, 2 pairs of jeans will cost 3x.

4 pairs of socks cost as much as one pair of jeans.

If 2 pairs of jeans cost 3x

Then 1 pair will cost 3x/2 = 1.5x

Thus, 4 pairs of socks will cost 1.5x.

Thus, 1 pair of socks will cost 1.5x/4

Then, 64 pairs of socks will cost;

64 × 1.5x/4 = 24x

Earlier, we saw that 1 coat costs 6x.

Thus means that;

Number of coats to exchange for 64 pairs of socks = 24x/6x = 4 coats

Circles in the Coordinate Plane
Acellus
Complete the equation of this circle:
А
1

Answers

Answer:

(x -+2)² + (y - 4)² = 36

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 2, 4) and r = 6 , then

(x - (- 2))² + (y - 4)² = 6² , that is

(x + 2)² + (y - 4)² = 36 ← equation of circle

Given that QR¯∥ST¯, identify the length of PT¯.

Answers

Answer:

PT = 16.3 units

Step-by-step explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]

[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]

[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]

[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]

[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]

PT = [tex]\frac{49}{3}[/tex]

PT = 16.3 units

42°
Х

please help with this

Answers

Answer:

X=48degrees.

Step-by-step explanation:

Sum of all angle of traingle=180degrees.

So, 90+42+X=180

132+X=180

X=180-132=48degrees

which of the following is a prime number (a).111 (b)91 (c).61 (d).51​

Answers

Answer:

(c).61

Step-by-step explanation:

61 is a prime number. The number is divisible only by 1 and itself.

Which of the following characteristics best describes the given function of
f(x) = -2x + 5 ?

A) minimum, always decreasing, exponential function

B) minimum, always decreasing, linear absolute value function

C) no maximum or minimum, always increasing, linear function

D) no maximum or minimum, always decreasing, linear function

Answers

Answer:

D

Step-by-step explanation:

the Negative sign in front of 2 shows the function is decreasing

What is (9.3x10^34) in scientific notation?
(3.1x 10^17) ​

Answers

Answer:

B

Step-by-step explanation:

3 x 10 ^17

Which is B

edit: So when doing scientific notation, you just divide the important first number of 9.3 or whatever by 3.1 like normal.

Then, when doing exponents, heres a rule of thumb.

When adding exponents, the base must be the same.

9.3 ^ 100  +  9.3 ^ 3  =  9.3 ^103

9.3 ^ 29 + 4.4 ^ 54 = cannot be solved

When subtracting exponents, the same rule applies as adding, the bases must be the same, otherwise, you just subtract or add like normal.

When dividing exponents, you just subtract exponents. The bases must be the same though of course.

3 ^ 30

----------

3 ^ 20

====  3 ^ 10

When multiplying exponents, you add exponents like normal. Bases are the same ect.

4 ^ 49    x    4 ^ 2   =   4 ^ 51

When doing scientific notation, the same rule applies.

The 10 is the base, so in your case, you divide the 9.3 and 3.1 like normal to get 3.

The exponent by the 10 is subtracted to get 17 since 34 - 17 = 17.

If g(x) = (x + 2)/3, find g(-8).

Answers

Answer:

-2

Step-by-step explanation:

Substitute -8 in place of x and you get (-8+2)/3 or -6/3 which is -2

Answer:

g(- 8) = - 2

Step-by-step explanation:

To find g(- 8) substitute x = - 8 into g(x) , that is

g(- 8) = [tex]\frac{-8+2}{3}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2

Of the 37 teachers at Francesca's high school, 9 are female. What is the ratio of the number of male teachers to the total number of teachers?

Answers

Answer:

28 : 37

Step-by-step explanation:

Find how many male teachers there are by subtracting 9 from 37:

37 - 9

= 28

Create a ratio with this to the total number of teachers:

28 : 37

So, the ratio of the number of male teachers to the total number of teachers is  28 : 37.

The Line segments are translated 2 units to the left to form A’B’ and C’D’. Which statement describes A’B’ and C’D’?

Answers

Answer:

Line segments A'B' and C'D' do not intersect and are the same distance apart as AB and CD.

Step-by-step explanation:

|x-2| + |x+1| -5=0
find x

Answers

Answer:

|x-2| + |x+1| -5=0

⇒|x-2| + |x+1|=5

⇒x-2+x+1=5

⇒2x=6

⇒x=3

Step-by-step explanation:

36. Given that y varies directly with x,
what is the equation of direct variation
if y is 3 when x is 7?

Answers

Answer:

A. y = 3/7x

Step-by-step explanation:

Direct variation: y = kx

3 = 7k

k = 3/7

y = 3/7x

Need help asap, thanks :)

Answers

Answer:

937

425

Step-by-step explanation:

9 is the square of 3

7 is 1 more than 6, the double of 3

4 is the square of 2

5 is 1 more than 4, 2x 2

Is there more?

Answer:

425

Step-by-step explanation:

1st = 2^2

3rd = 2*2 + 1

please please jhelp me....​

Answers

Answer:

2·v - (u + w) = (5, 0, -10)

Step-by-step explanation:

The given values of the vectors are;

u = (2, -1, 3), v = (4, 0, -2), and w = (1, 1, 3)

The required vector is 2·v - (u + w)

2 × v = 2 × (4, 0, -2) = (8, 0, -4)

(u + w) = (2, -1, 3) + (1, 1, 3) = (3, 0, 6)

Therefore;

2·v - (u + w) = (8, 0, -4) - (3, 0, 6) = (5, 0, -10)

2·v - (u + w) = (5, 0, -10)

Help me please, this all is of 4 marks​

Answers

Step-by-step explanation:

1) 250 n(tnc)

2) 100

this your answer

A ∆ has Č = 90°, Â = 26° and = 30, Find the Angle BC, Side AB and BC.

Answers

Answer:

B = 64°

AB = 33.378

BC = 14.632

Step-by-step explanation:

Given the right angled triangle ;

Angle B = 180 - (90 + 26) (sum of angles in a triangle)

Angle B = 180 - 116

Angle B = 64°

Side AB = c

Using trigonometry :

Sin B = opposite / hypotenus

Sin 64 = 30/AB

AB = 30 / Sin64

AB = 33.378

Side BC ;

Sin A = BC / AB

Sin 26 = BC / 33.378

BC = 33.378 * Sin 26

BC = 14.632

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