Given: angle LMN is congruent to angle LNM; angle MPN is congruent to angle NOM

Prove: MP is congruent to NO

Given: Angle LMN Is Congruent To Angle LNM; Angle MPN Is Congruent To Angle NOMProve: MP Is Congruent

Answers

Answer 1

The prove that segment MP is congruent to segment NO (MP ≅ NO) can be presented as follows;

Statement [tex]{}[/tex]                             Reasons

1. ∠LMN ≅ ∠LNM [tex]{}[/tex]                 1. Given

∠MPN ≅ ∠NOM

2. MN ≅ MN  [tex]{}[/tex]                        2. Reflexive property

3. ΔMNP ≅ ΔNMO [tex]{}[/tex]               3. SAA congruency postulate

4. MP ≅ NO  [tex]{}[/tex]                         4. CPCTC

What are congruent segments?

Two segments are congruent if they have the same length

         

The known relationships between the measures of the angles are;

∠LMN ≅ ∠LNM

∠MPN ≅ ∠NOM

Required to prove that MP ≅ NO

The two column method can be used to prove the congruency of the sides MP and NO as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. ∠LMN ≅ ∠LNM         [tex]{}[/tex]                1. Given            

∠MPN ≅ ∠NOM

2. MN ≅ MN     [tex]{}[/tex]                            2. Reflexive property of congruency

3. ΔMNP ≅ ΔNMO     [tex]{}[/tex]                  3. SAA congruency rule

4. MP ≅ NO     [tex]{}[/tex]                             4. CPCTC

Details of the above postulates and rules used to prove the congruency of the segments MP and NO are as follows;

SAA congruency postulate

The SAA (SAA is an acronym for Side-Angle-Angle) congruency postulate states that if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent. It indicates that if two triangles are congruent, then, their corresponding sides are also congruent.

Learn more on triangle congruency rules here: https://brainly.com/question/14818583

#SPJ1


Related Questions

Determine the length of PN and the value of y

Answers

Answer:

Side PN=26

y=16

Step-by-step explanation:

I put a photo of my work. It’s easier to do that then to try and put it all in words

rewrite 1/2 3/4 as a unit rate

Answers

Answer: 3 / 8

Step-by-step explanation:

Answer:

The answer is 6:1

Step-by-step explanation:

Write a rule for the linear function shown in the graph.


y = 4x – 3


y = –x + 4


y = 2x + 5




y = 1/4x +1

Answers

Answer: Answer is A. y = 4x - 3

Graph the line using the slope and y-intercept, or two points.

Slope:  2/ 5

y-intercept:  ( 0 , − 1 )

x           y

0          − 1

5/ 2       0

Step-by-step explanation:

How do you graph y=4x-3?

In graphing an equation, a very valuable graphing technique is the ability to recognize the kind of graph that a certain type of equation produces.

Any equation that is of the form y = mx + b is in the "slope-intercept" form for the equation of a straight line, where x and y are variables, where “m” is a real number representing the slope of a line, and where “b” is a real number representing the y-intercept of a line , i.e., the y-coordinate of the point of intersection between a straight-line graph and the y-axis.

Since the given equation y = 4x ‒ 3 is in the slope-intercept form, where m = 4 and b = ‒3, then it’s a linear equation and its graph is a straight line. Also, looking at the given equation, we know that the independent variable x can take on any real number as a replacement.

Now that we know that the graph of the given equation is a straight line and that there are no restrictions on the variable x, we need to determine and then draw the straight-line graph on a Cartesian (rectangular) coordinate system with the y-axis as the vertical axis and the x-axis as the horizontal axis. We know that two points determine a straight line; So, all we need to do is find the point where the straight-line graph of the given equation y = 4x ‒ 3 intersects the x-axis, i.e., the point of the x-intercept, and find the point where the straight-line graph of y = 4x ‒3 intersects the y-axis, i.e., the point of the y-intercept. Also, it would be a good idea to plot a third point as a check.

(1.) Determining the point of the x-intercept:

For any point on the x-axis, the y-coordinate is zero; therefore, in our given equation, let y = 0 and solve for x as follows:

y = 4x ‒3

0 = 4x ‒3

0 + 3 = 4x ‒3 + 3

(1/4)(4x) = (1/4)(3)

x = 3/4

Therefore, the x-intercept is x = 3/4, and the graph of the given equation y = 4x ‒3 intersects the x-axis at the point (3/4, 0).

(2.) Determining the point of the y-intercept:

To get the y-intercept, we can simply select it from the given equation y = 4x ‒3 which is already in slope-intercept form (y = mx + b), i.e., y = 4x ‒3 or y = 4x + (‒3); therefore, the y-intercept of the straight-line graph of the given equation is y = b = ‒3, which is the y-coordinate of the point of intersection between the straight-line graph of the given equation and the y-axis. Also, for any point on the y-axis, the x-coordinate is zero; therefore, the straight-line graph of the given equation intersects the y-axis at the point (0, ‒3).

(3.) Check Point

In generating a third point as a check point, choose a convenient value for x so that the corresponding value for the dependent variable y is nice and even. Let x = 2, then:

y = 4x ‒3

= 4(2)‒ 3

= 8 ‒ 3

y = 5

Consequently, the third point (check point) on the straight-line graph of the given equation is (2, 5).

(4.) Plot the points

Now, create the straight-line graph of the given equation by plotting the three points: (3/4, 0), (0, ‒3), and (2, 5) on a Cartesian (rectangular) coordinate system, and then use a straight edge to draw the straight line through all three plotted points. Draw the line past the two outer points and then draw an arrowhead at each “end” of the line to show that the line goes on indefinitely in both directions. NOTE: If the third point (2, 5)(the check point) is not on the drawn line, then go back and look for an error. The error was either made in finding the x- and y-intercepts, or the error was made in generating the coordinates of the check point, or both. When the error is found, make the appropriate correction(s), and then redraw the graph (straight line) of the given equation.

These are four steps that you can use to graph the given equation y = 4x ‒3 or any equation that is in the slope-intercept form for the equation of a straight line: y = mx + b.

a glass jar has 64 chocolate. mark, dave and ralph will share the chocolate in the ratio of 1:1:2, how many chocolates will each one of them get?​

Answers

Step-by-step explanation:

64/(1+1+2)

= 64/4

= 16

1 : 1 : 2

mark = 1×16 = 16

dave = 1×16 = 16

ralph = 2×16 = 32

Step-by-step explanation:

hope it helps

please rate

Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.

30 + 15 x greater-than-or-equal-to 90

Which best describes the restrictions on the jobs Deepak will accept?
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.

Answers

The answer is “He only accepts jobs that last 4 or more hours.”

Answer:

4 or more hours

Step-by-step explanation:

I just took the test

Can some one help please

Answers

Answer:

y=7x+6

Step-by-step explanation:

hope i helped

Solve the inequality.
20 + 8.1 > 28

Answers

Answer:

You can't solve since there is no variables

The inequality from the question is true

Find the 10th term of the following geometric sequence.
2, 6, 18, 54,
.

Answers

Step-by-step explanation:

the formula to calculate number of terms in GP is : TN=a×r^n-1

compare the rates to find which is greater.
50 envelopes for $2.49 or
90 envelopes for $5.50

Answers

We describe this as cost per envelope which tells you the cost gets divided by the number of envelopes.

$2.49/50 = 0.0498 cents per envelope

$5.50/90 = 0.0611 cents per envelope.

So the 90 for $5.50 costs more per envelope than the 50 for $2.49

A number line going from negative 3 to positive 3 in increments of 1.
Which statements are true? Check all that apply.
Negative 2.5 = negative 2 and one-half
–1.5 > –0.5
–0.5 < 0
–2.5 < –2
1 and one-half greater-than 1.5

Answers

Answer:

1., 3., and 4.

Step-by-step explanation:

It's C.  

Or how other people say it,

3 or –2.5 < –2

PLZ HELP FAST IM CONFUSED

Answers

480 i think not sure

help this makes no sense to me and its due in 1 day

Answers

First we can find the line RT which is the square root of 40^2-32^2 which is equal to 24.

RT=24

Right Triangle Altitude Theorem Part: The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

The geometric mean of 32 and TS is 24, so set up equation.

2nd root or square root of 32*TS=24

32*TS=576

TS=18

QS=18+32=50

I hope this answer helped if you have any questions feel free  to ask me in the comments.


find the value of the expression :
[tex]{x}^{2} + 2xy + {y}^{2} [/tex]


[tex]y = \frac{3 + i }{i} \\ x = 2 + 3i[/tex]

Answers

Answer: x² + 2xy + y² = 9

x² + 2xy + y² = (x + y)²

with x = 2 + 3i and y = [tex]\frac{3+i}{i}[/tex], we have:

[tex](x + y)^{2}=(2+3i+\frac{3+i}{i})^{2}\\\\=(\frac{2i+3i^{2}+3+i }{i})^{2}\\\\=(\frac{3i-3+3}{i})^{2} \\\\=(\frac{3i}{i})^{2}\\\\=3^{2}=9[/tex]

Step-by-step explanation:

How do you solve -8 -x = x -4x

Answers

Answer:

hey there

x = 4

Step-by-step explanation:

Let's solve your equation step-by-step.

−8−x=x−4x

Step 1: Simplify both sides of the equation.

−8−x=x−4x

−8+−x=x+−4x

−x−8=(x+−4x)(Combine Like Terms)

−x−8=−3x

−x−8=−3x

Step 2: Add 3x to both sides.

−x−8+3x=−3x+3x

2x−8=0

Step 3: Add 8 to both sides.

2x−8+8=0+8

2x=8

Step 4: Divide both sides by 2.

2x/2  = 8/2

x= 4

have a good day!!!

Answer:

x= 4

Isolate the variable by dividing each side by factors that don't contain the variable.

PLS, HELP is it A. B. C. D.

Answers

Answer:

May be c but I am not sure dear.

122 cats
Mrs. Roberts is 3 times as old as her son. The sum of their ages is 48 years.
How old was Mrs. Roberts when her son was born?

Answers

Answer:

24

Step-by-step explanation:

To find how old Mrs. Roberts was when her son was born, we first need to know both of their ages. I'm going to give Mrs. Roberts the variable m and her son the variable s.

Let's turn the two sentences about their ages into equations:

m=Mrs. Roberts and 3s= three times as old as her son

m=3s

m+s is the sum of their ages

m+s=48

Now substitute the first equation into the second one:

m+s=48

(3s)+s=48

4s=48

s=12

The son is 12 years old. Now substitute s into one of the equations to solve for the mother's age:

m=3s

m=3(12)

m=36

Mrs. Roberts is 36. Since they are asking how old she was when her son was born, we will subtract her son's age from her age, since she would be 12 years younger:

36−12=24

Mrs. Roberts was 24 when her son was born.

credit to CountryGirl on Socratic Q&A

Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.

The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.

How many pounds of potatoes does Mrs. Hanson need?

Enter your answer as a mixed number in simplest form by filling in the boxes. please hurry dont say what to add or mutply say the answer i am on k12

Answers

Answer:

3 9/16 lbs

Step-by-step explanation:

took quiz

What is the area of the composite figure

Answers

Answer:

32

Step-by-step explanation:

ddd345

If Danielle can spend no more than $75 on clothes, and wants a pair of shoes for $40 and will spend the rest of the money on $12 scarves, what is her rate of change ?

Answers

Answer:

$6

Step-by-step explanation:

$75 - $40 = $30

With $30, the maximum number of scarves you can get is 2.

$30 - $24 = $6

Hope that helps!

Step-by-step explanation:

$6

the max number of scarves she can get is 2

hope this helps

Drag the top of the rectangle up and down in the tool below to explore the
functional relationship between the two shapes.
The ? is a function of the ?

Answers

Answer:

A.

Step-by-step explanation:

i just took it

Answer:

the answer is c I just did the test

Jackson hikes 220.2 meters up a mountain. If he is 60% of the way up, how tall is the mountain? 132.12 meters

Answers

Answer:

367meters

Step-by-step explanation:

220.2 = 0.6 * h

220.2/0.6 = 0.6 * h / 0.6

367 = h

367 meters

-(7p+6)-2(-1-2p) what is that simplified pls help! And explain

Answers

Answer:

-3p-4

Step-by-step explanation:

-(7p+6)-2(-1-2p)

-7p-6+2+4p

-7p+4p-6+2

-3p-6+2

-3p-4

in a survey about favorite breakfast foods 3/8 of those surveyed chose cereal,0.125 chose yogurt 0.1875 chose fruit and 5/16 chose toast wihch food got least numbers of votes

Answers

cereal is the least amount of numbers

give all relationships between angle 1 and angle 2 select all that apply​

Answers

Answer:

vertical maybe if try it and see

So hard. Dont reports I actually cant take the pictures off, I needed help with a question but they dont come off. Also what's the square root of 282.93?

Answers

Answer:

whegvrjrbel)hbrbeueuejneje

The square root of 16.82

A rectangle is 2/5 inches long and 1/3 inches wide. What is the area of the rectangle?

Answers

Step-by-step explanation:

2/5 x 1/3 = 2/15 inches squared

Radius is 8 ft. whats the answer

Answers

Answer:

Area = 64pi, Circumfrence=2pi(8)

Step-by-step explanation:

Answer:

Depends. Down below.

Step-by-step explanation:

It depends.

Area of the circle = [tex]\pi[/tex] x [tex]8^{2}[/tex] ≈ 201.06 ft

Circumference of the circle = 2 x [tex]\pi[/tex] x 8 ≈ 50.27 ft

find the common factors of the given terms 1. 12x, 36. 2. 2y, 22x. 3. 14pq, 28p^2 q^2​

Answers

Answer:

answer 1. 12. 2nd is 2. and 3rd is 14pq

hope it helps

solve for x or find x ​

Answers

Answer:

x = 18

Step-by-step explanation:

diagonals bisect each other so 12x = 216

x = 216/12

x = 18

If using the method of completing the square to solve the quadratic equation x^2-20x+33=0x
2
−20x+33=0, which number would have to be added to "complete the square"?

Answers

Answer:

The complete square of the given quadratic equation

( x - 10)² = 67

The solution of the quadratic equation

  x = 18.2     and x = 1.8

Step-by-step explanation:

Step(i):-

Given that the quadratic equation

         x² - 20 x +33 =0

         x² - 2(10) x +(10)²-(10)²+ 33 =0

By using (a-b)² = a² -2ab + b²

       ( x - 10)² -100 +33 =0

         ( x - 10)² - 67 =0

        ( x - 10)² = 67

Step(ii):-

The complete square   (x - 10)² = 67

                                     x -10  = ±√67

                                    x -10 = ± 8.1853

                      x -10 = 8.2   and x -10 = -8.2

                      x = 10+8.2   and x = 10 -8.2

                      x = 18.2     and x = 1.8

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