In triangle ABC points M and N lie on sides AB and BC, respectively such that MN∥ AC . Segments AN and CM intersect at point K and AK = KC. Prove that △ABC is isosceles.

Answers

Answer 1

Answer:

                 Statements                                                   Reasons

1. [tex]MN \parallel AC[/tex]                                                    1. Given

2. [tex]AK = KC[/tex]                                                  2. Given

3. [tex]m \angle NAC = m\angle MCA[/tex]                                 3. Base angles theorem.

4.  [tex]m \angle NAC = m\angle MNA[/tex]                               4. Alternate interior angles.

5. [tex]m \angle MCA = m \angle NMC[/tex]                               5. Alternate interior angles.

6. [tex]MK = NK[/tex]                                                6. Isosceles triangle theorem.

7. [tex]m \angle MKA = m \angle NKC[/tex]                               7. Vertical angles.

8.  [tex]\triangle MKA \cong \triangle NKC[/tex]                                   8. By SAS postulate.

9. [tex]m \angle MAK = m \angle NCK[/tex]                               9. By CPCTC.

10.                                                                  10. Sum of adjacent angles.

[tex]m\angle MAK + m \angle NAC = m \angle NCK + m \angle MCA\\m \angle A = m \angle C[/tex]

11. [tex]\triangle ABC[/tex] is isosceles                                  11. Base angles theorem.

 In Triangle ABC Points M And N Lie On Sides AB And BC, Respectively Such That MN AC . Segments AN And

Related Questions

plz help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

88 inches

Step-by-step explanation:

The given bicycle has a tyre that is 28 inches in diameter.

How far the bicycle moves forward each time the wheel goes around is the circumference of the bicycle tyre.

This is calculated using the formula:

C =\pi \: d

We substitute the diameter and

\pi =  \frac{22}{7}

C =  \frac{22}{7}  \times 28

This simplifies to

C =22 \times 4

88 \: inches

Language arts test is worth 100 points there is a total of 26 question There are spelling words question that I wasn't points each in vocabulary words question worth five points each how much of each type of question are there

Answers

Answer: There are 10 two points and 16 five points questions.

Step-by-step explanation:

This is the detailed question:

A language arts test is worth 100 points. There are a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question is there?

Let y = the number of 2 points questions

Let z = the number of 5 points questions

y + z = 26 ......... i

2y + 5z = 100 ........ ii

Multiply equation i by 2

Multiply equation ii by 1

2y + 2z = 52 ......... iii

2y + 5z = 100 ....... iv

Subtract iv from iii

-3z = -48

z = 48/3

z = 16

Since y + z = 26

y = 26 - 16

y = 10

y = 10 two points questions

z = 16 five points questions

There are 10 two points and 16 five points questions.

Solve for x in the following figure.

Answers

Answer:

x=80°

Step-by-step explanation:

supplementary angles equal 180°

∠J=80

80+x+20=180

100+x=180

x=80

NEED ANSWER ASAP
For the function
f(x) = |x|-2, find the value when x = -3

Answers

Answer:

1

Step-by-step explanation:

The absolute value of -3 is just 3, because it has a distance of 3 away from 0. Therefore, [tex]\mid -3 \mid -2=3-2=1[/tex]. Hope this helps!

Solve the quadratic by factoring.
x2 - 4x = -4x + 4

Answers

Answer:

x=2 or x=-2

Step-by-step explanation:

ax^2+bx+c=0

first we rearrange this equation so we get x^2+(-4+4)x-4=0 so its x^2-4=0 so that means b=0 now we should find two numbers that when we multiply them we get c and when we subtract them we get b so that two numbers are 2 and -2

What is the axis of symmetry for the function f(x)=7-4x+x2?
X=-3
x = -2
x = 2
x= 3

Answers

Answer:

x = 2

Step-by-step explanation:

C on edg 2020

The axis of symmetry of f(x) = 7-4x + x^2 is x = 2

How to determine the axis of symmetry?

We have:

f(x) = 7-4x + x^2

Differentiate the function

f'(x) = -4 + 2x

Set the function to 0

-4 + 2x = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2

Hence, the axis of symmetry of f(x) = 7-4x + x^2 is x = 2

Read more about axis of symmetry at:

https://brainly.com/question/15709421

#SPJ9

rectangle with length 11 1/2 in. and width 8 in The area of this rectangle is____________
in2.

Answers

Answer:

Step-by-step explanation:

look, area = length x width

so that means that the area of this rectangle is

= 11 1/2 * 8

= 23/2 * 8

= 23 * 4 (simplified)

= 92 in^2

Answer:

[tex]92in.^{2}[/tex]

Step-by-step explanation:

Area of a rectangle= L×W

If length= 11[tex]\frac{1}{2}[/tex]in. and width= 8in.,

∴ Area = 11[tex]\frac{1}{2}[/tex]in. × 8in.

           = [tex]\frac{23}{2}[/tex] × [tex]\frac{8}{1}[/tex] [tex]in.^{2}[/tex]

           = (23 × 4) [tex]in.^{2}[/tex]

           = 92[tex]in.^{2}[/tex]

Hope this helps!!!

 

What is the slope of the line that passes through the points (-2, 7) and (2,-5)?
Write your answer in simplest form.​

Answers

Answer:

Denote that line: y = ax + b

Line passes (-2, 7) and (2,-5):

=> -2a + b =7

=>  2a + b = -5

Add both side of above equations:

=> 2b = 2

=> b = 1

=> a = (-5 - 1)/2 = -3

=> Slope a = -3

Hope this helps!

:)

This question is based on the equation of line. Therefore, the slope of the line is -3 that passes through the points (-2, 7) and (2,-5).

Given:

Points are (-2, 7) and (2,-5).

We need to calculate the slope of the line that passes through the points (-2, 7) and (2,-5).

According to the question,

As we know that, equation of line: y = mx +c

It is given that, line passes through points, (-2, 7) and (2,-5).

Now, putting this points in equation of line: y = mx +c.

We get,

=> -2m + c =7                                   ...(1)

=> 2m + c = -5                                ...(2)

Now, adding and solving above two equations,

We get, c = 1

Then, putting  the value of b= 1 in equation (1).

We get, m = -3.

Therefore, the slope of the line is -3 that passes through the points (-2, 7) and (2,-5).

For more details, prefer this link:

https://brainly.com/question/21511618

How many solutions does this equation have?

–8 + t = –t + 10

Answers

Answer:

One

Step-by-step explanation:

Since (1) is the highest exponent value, there can only be one solution.

IF t^2 then there would be two answers.

Answer:

One solution

Step-by-step explanation:

To find the amount of solutions, you must solve first:

-8 + t = -t + 10

First, add t to both sides:

-8 + 2t = 10

Add 8 to both sides:

2t = 18

Divide both sides by 2:

t = 9

Since there has been a solution to this equation, that means there's only one solution.

A circular rug has the radius of 4 feet. Which of the following is closest to the number of square inches the rug covers.

A. 55.26 ft2

B. 50.24 ft2

C. 29.7 ft2

D. 33.6 ft2

Answers

Answer:

B. 50.24ft

Step-by-step explanation:

A=(pie)r^2

A=3.14(4)^2

A=3.14 * 16

A=50.27

Closest to 50.24

The ratio of men to women is 5 to 8. If there are 286 employees total how many women work for the company ??
Please answer

Answers

Answer:

There are 176 women in the company.

Step-by-step explanation:

Let number of men are 5x and number of women are 8x.

Total number of employees in the company are 286.

But according to given condition, total no of employees are :

[tex]5x+8x = 286\\\\13x=286\\\\x=\dfrac{286}{13}\\\\x=22[/tex]

Total no of women are 8x. It means [tex]22\times 8=176[/tex]. Hence, there are 176 women in the company.

Duffy completed a 50-meter dash in 36 seconds. That was 90 percent of the time it took Paul to complete it. What was Paul's time?
42 seconds
38 seconds
40 seconds
36 seconds

Answers

Answer:

40 seconds

Step-by-step explanation

Luke bought three canvas boxes to store his papers. The canvas boxes have dimensions of 12 inches by 10 inches by 12 inches. What volume of itmes can be the three canva boxes hold?

Answers

Given Information:

Number of boxes = 3

Length of boxes = L = 12 inches

Width of boxes = W = 10 inches

Height of boxes = H = 12 inches

Required Information:

Volume of items boxes can hold = ?

Answer:

[tex]Volume = 4320 \: in^{3}[/tex]

Step-by-step explanation:

We are given that Luke bought 3 canvas boxes to store his papers.

We are also provided the dimensions of boxes.

We are asked to find out the volume of items that can be stored by these 3 canva boxes.

A canva box has shape of a rectangular prism and its volume is given by

[tex]Volume = L \times W \times H[/tex]

Where L is the length of the box, W is the width, and H is the height of box.

[tex]Volume = 12 \times 10 \times 12 \\\\Volume = 1440 \: in^{3}[/tex]

So the volume of 3 boxes is

[tex]Volume = 3\times 1440 \\\\Volume = 4320 \: in^{3}[/tex]

Therefore, the 3 canva boxes can store 4320 cubic inches of volume.

Answer:

D) 4,320

Step-by-step explanation:

ession r' - (3+2)
(3 + 2)2 for 2 = 4.

Answers

Answer:

Step-by-step explanation:

idk im aooy

hey can anyone pls help me out in dis pls i will mark u as brainliest!!!!! and i will give 30 points

Answers

Answer:

graph b because its a parabola

Step-by-step explanation:

Answer:

Graph B does not belong

Step-by-step explanation:

All the other graphs are linear inequalities, whereas graph B is a quadratic inequality. You can also tell by how they look. The straight lines are linear, and the symmetric curve (parabola) is a quadratic

Phoebe built the sandbox below for her younger sister.
2 feet
4 feet
5 feet
What is the volume of the sandbox?

Answers

I think its 40ft i hope it helps

Answer: 40 feet

Step-by-step explanation:  Volume = length * width * height

then substitute Volume = 2 * 4 * 5

multiply Volume = 8 * 5

multiply again Volume = 40

hope this helps mark me brainliest if it did have a great day

3.64 divided by 60.5 ROUNDED plz answer!!!

Answers

Answer:

0.06

Step-by-step explanation:

How would you find the area of this?

Answers

the formula for it is bh , multiply 14 by 24 and the answer is 336

Consider circle A in the diagram below where the m∠DCG=25∘ and mCF^=60∘ and prove that m∠EDF=55∘.

Given that m∠DCG=25∘, this angle intercepts arc DG^ which makes mDG^=_, this means that mED^=130∘ as EG^ is a diameter.

∠CED intercepts CFD^, which makes m∠CED=_.

∠ECD intercepts ED^ which makes m∠ECD=_.

∠CDF intercepts CF^ which is 60∘, making m∠CDF=30∘. Using the triangle sum theorem, m∠EDC=_, and using Angle addition postulate the m∠EDF=55∘.

Answers

Answer:

50, 90, 65, 25

Step-by-step explanation:

I dont know how to get to it that is why I searched it up :/

John made 2 quarts of juice for a school party. He said that he made 2/4 cup of juice. A. Explain John's mistake. B. How many cups of juice did John actually make?

Answers

Answer:

A. He thought 1 quart = 1/4 cup

B. actually made 8 cups of juice

Step-by-step explanation:

From conversion,

1 cup =1/4 quarts

A. John thought 1 quarts = 1/4 cup, which was his mistake

B. His 2/4 cups is actually

4*2 = 8 cups

A school dedicated 50% of the courtyard area for students to start a garden. The students want to know how much of the 632-square-foot space they will be able to use.

Answers

Answer:70

Step-by-step explanation:

Answer:

this is SUPER late but it is 1/2 x 632

Step-by-step explanation:

which quadrilateral always has diagonals that are congruent but not necessarily perpendicular?

a) parallelogram
b) rectangle
c) rhombus
d) square

Answers

Answer:its a rectangle

Step-by-step explanation:

Which of the following is the quotient of the rational expressions shown
below?

Answers

Answer :
A

Explanation:

3. The measure of each inscribed
angle is equal to( )times the
measure of the intercepted arc.
a. 1/2
b. 1
c. 2

Answers

Answer: A. 1/2

Step-by-step explanation:

A piepie is divided into 2020 equal pieces. GlennGlenn and SophieSophie each ate one fourth 1 4 of the piepie on MondayMonday. The next​ day, SophieSophie ate one fifth 1 5 of the piepie that was leftover. How many of the pieces of the original piepie ​remain? Explain your reasoning. ​Together, GlennGlenn and SophieSophie ate one fourth 1 4 ​piece(s) on MondayMonday​, and SophieSophie ate one fifth 1 5 ​piece(s) the next day. To find the number of pieces that​ remain, add these numbers to the total number of pieces.​ So, 0.450.45 pieces of the original piepie remain.

Answers

Answer:

Pieces remaining =  1 - (1/4 + 1/4) - (1/2 x1/5) = 1/2 - (1/2 x1/5) = 1/2 - 1/10 = 4/10

Therefore, 4/10 x 20 = 8 pieces.

Step-by-step explanation:

Sophie ate 1/4 = 5 pieces

Glenn ate 1/4 = 5 pieces

Remaining pieces = 20 - 5 - 5 = 10 pieces

On Monday, Sophie ate = 1/5 x 10 = 2 pieces

Therefore, remaining pieces = 10 - 2 pieces = 8 pieces

Sophie and Glenn consumed half of the pie the first day.  This is equal to 10 pieces.  The remaining pieces will be 10.  If, on Monday, Sophie ate 1/5 of 10 pieces, representing 2 pieces, the number left over is 10 Minus 2, which equals 8 pieces.

Prodigy math i will mark you brainliest if you get it right

Answers

Answer:

8 and 2/8

Step-by-step explanation:

3 and 2/8 times 2 is 6 and 4/8 then u subtract that from 14 and 6/8

Answer:

1 is 18, and 2 is 36 brainliest

Step-by-step explanation:

Help meeee!!! Whats x

Answers

Answer:

74°

Step-by-step explanation:

The angle on a line = 180°

therefore:.

x + 106° = 180°

x = 180° - 106°

x = 74°

Answer: 74 degrees.

Step-by-step explanation:

Angles on the same side of a line add to 180.

The angle measure of 106 and the angle measure of x lie on the same side of the line WZ, so you can add them both to get 180:

106 + x = 180

x = 74

what’s the solution

Answers

Answer:

We need more info

Step-by-step explanation:.

You roll a number cube 20 times. Which scenario is least likely?

Answers

Answer:

you won't roll the same number 5 times

Today, there were 2 members absent from the band. The present members folded 25 programs each, for a total of 525 programs. How many members are in the band when no one is absent…

Answers

Answer:

23

Step-by-step explanation:

225/25 = 21

21+2=23

Answer:

How many members are in the band when no one is absent?

the answer is c if you are refering to the khan academy question

Step-by-step explanation:

its from khan academy

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