How do I prove my SSS postulate?
Answers
The SSS postulate states that "if all the three sides of a triangle are equal to the sides of another triangle then the given triangles are congruent" is proved.
Assume that the lengths of all three sides of the triangles ABC and DEF are known.
The diagram is attached at the end of the solution.
Pick a side from triangle ABC. Find the side with the same length as triangle DEF. For example, we pick [tex]\overline{AB}[/tex] and find that [tex]\overline{D E}[/tex] is equivalent in length to [tex]\overline{AB}[/tex].
Next, write a proof statement about our conclusion and the reason for it. For the reason clause, we state that the two sides are given, since no other work was involved besides reading the lengths of the sides of the diagram. The three dots in the upside-down triangle means "because".
[tex]$$\overline{AB} \cong \overline{DE}$$[/tex]
Choose the other side from triangle ABC. Find the side with the same length as triangle DEF.
We choose the second side [tex]\overline {BC}[/tex] and find from the diagram that [tex]\overline{EF}[/tex] has the same length. The proof statement for this step is:
[tex]$$\overline{BC} \cong \overline{EF}$$[/tex].
Step 3: Pick the last side from triangle ABC. From triangle DEF, identify the side that is the same length. [tex]\overline{AC}[/tex] and [tex]\overline{DF}[/tex] have the same length. We add another proof statement.
[tex]$$\overline{AC} \cong \overline{DF}$$[/tex]
Step 4: We've discovered that the two triangles have three pairs of congruent sides. That means, by the SSS congruence theorem, triangles ABC and DEF are congruent.
Add a proof statement for this conclusion. The list of the proof statements looks like this.
[tex]$\overline{AB} \cong \overline{DE}[/tex] because [tex]\overline{AB}$[/tex] and [tex]$\overline{DE}$[/tex] are given.
[tex]$\overline{BC} \cong \overline{EF}[/tex] because [tex]$\overline{BC}$[/tex] and [tex]$\overline{EF}$[/tex] are given.
[tex]$\overline{AC} \cong \overline{DF}[/tex] because [tex]$\overline{AC}$[/tex] and [tex]$\overline{DF}$[/tex] are given.
[tex]$\triangle A B C \cong \triangle D E F$[/tex] by SSS congruence theorem.
We have proved that the SSS congruence theorem holds for triangles ABC and DEF.
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Related Questions
Write a polynomial equation for a graph that passes through the point (-1, 60) and has three x-intercepts: (-4,0),
(1, 0), and (3, 0)
Answers
Given:
A graph of a polynomial passes through the point (-1, 60) and has three x-intercepts: (-4,0), (1, 0), and (3, 0).
To find:
The equation of the polynomial.
Solution:
A polynomial is defined as:
[tex]P(x)=a(x-c_1)(x-c_2)...(x-c_n)[/tex]
Where, a is a constant and [tex]c_1,c_2,...,c_n[/tex] are the zeros of the polynomial.
The given polynomial has three x-intercepts (-4,0), (1, 0), and (3, 0). It means [tex]-4,1,3[/tex] are the zeroes of the given polynomial and [tex](x+4),(x-1),(x-3)[/tex] are the factors of the given polynomial.
So, the equation of the polynomial is:
[tex]P(x)=a(x+4)(x-1)(x-3)[/tex] ...(i)
It passes through the point [tex](-1,60)[/tex].
[tex]60=a(-1+4)(-1-1)(-1-3)[/tex]
[tex]60=a(3)(-2)(-4)[/tex]
[tex]60=24a[/tex]
Divide both sides by 24.
[tex]\dfrac{60}{24}=a[/tex]
[tex]2.5=a[/tex]
Putting [tex]a=2.5[/tex] in (i), we get
[tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex]
Therefore, the equation of the given polynomial is [tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex].
work out the equation for each graph in the form
y=mx+c
please help !
Answers
Answer:
Top first one is y=-3x-3.
Step-by-step explanation:
I know you will be able to figure out the rest. I will explain. The problem if I just give you the answers are you won’t be actually able to solve it when you encounter it on like a test or something.
The explanation:
m=rise/run.
c=y intercept/ where it is on the y-axis.
if you go down on the y axis, it would negative. The opposite will be true if you go up.
I also think it is supposed to be y=Mx+b instead of y=Mx+c.
hopefully that made sense.
HELP PLEASE.
Area=
If there is no value under the square root enter a 1.
Answers
10^2+16^2=100+256=356^2
The first box should be 2 and the second should be 356
Plz help i don't wnat links i want you to show the answer on here i trust you will.
A=__in^2 i will give the brainlist 20 points btw
Answers
Answer:
a to L is 12 inches and a to n is 32 in Step-by-step explanation:
If ∠1 and ∠2 are complementary angles, and m∠1 = 74°; find m∠2
Answers
Answer:
m∠2 = 16°
Step-by-step explanation:
m∠1 + m∠2 = 90°
(Complementary angles)
74° + m∠2 = 90°
m∠2 = 90° - 74°
m∠2 = 16°
The measure of the angles 2 is 16 degrees
How to find complementary anglescomplementary angles sum up to 90 degrees.
Given one of the angles to be 74 degrees, hence;
m<1 + m<2 = 90 degrees
74 + m<2 = 90
m<2 = 90 - 74
m<2 = 16 degrees
Hence the measure of the angles 2 is 16 degrees
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which two ratios represent quantities that are proportional?
Answers
Answer:
C, because it equals in both sides
Answer:
The answer is C
Step-by-step explanation:
What is the inverse you would use to solve this problem: c/2=16
Answers
Answer:
multiplication
Step-by-step explanation:
What's the domain and range of the exponential growth function? (please help asappp no spam please or links or anything like that!!! will give brainliest)
Domain: All real numbers; Range: All real numbers
Domain: x > –2; Range: y > –2
Domain: x < –2; Range: All real numbers
Domain: All real numbers; Range: y > –2
Answers
Answer:
Domain: All real numbers; Range: y > –2
Step-by-step explanation:
Asymptote is y = -2 so all y-values have to be greater than -2. The asymptote is horizontal so x-values can be all real numbers.
Paul and his family are discussing how to pay for his college education. The cost of tuition at the college that Paul wants to attend is $9,000 per year. Paul’s parents will pay 85% of the tuition cost every year, and he will pay the rest. Paul has one year to save enough money to attend her first year of college. What is the minimum amount of money he should save every month in order to reach her goal?
Answers
Answer:
i think its 637
Step-by-step explanation:
Two similar cylinders have heights of 3 cm and 6 cm respectively. If the volume of the smaller cylinder is 30 cm3, find the volume of the larger cylinder.Required to answer. Single line text.
Answers
Answer:
Volume of big cylinder = 1,438.76 cm (Approx.)
Step-by-step explanation:
Given:
Height of smaller cylinder = 3 cm
Height of big cylinder = 6 cm
Volume of smaller cylinder = 30 cm³
Find:
Volume of big cylinder
Computation:
Volume of smaller cylinder = πr²h
(22/7)(r²)(3) = 30
Radius of small cylinder = 1.783 cm (Approx.)
So,
Radius of big cylinder = 1.783 x 2 = 3.566 cm (Approx.)
Volume of big cylinder = πr²h
Volume of big cylinder = (22/7)(3.566)²(6)
Volume of big cylinder = 1,438.76 cm (Approx.)
Un distribuidor debe repartir 879 botellas de cerveza entre 3 bares. Si el pedido del bar A es la mitad que el del bar B y la cuarta parte del bar C. ¿Cuántas botellas le tocan a cada bar?
Answers
Answer:
Total number of bottles Bar A get = 126
Total number of bottles Bar B get = 251
Total number of bottles Bar C get = 502
Step-by-step explanation:
Given - A distributor must distribute 879 bottles of beer among 3 bars. If the order of bar A is half that of bar B and a quarter of bar C.
To find - How many bottles do each bar get?
Proof -
Let us assume that
Total number of bottles Bar A get = x
Total number of bottles Bar B get = y
Total number of bottles Bar C get = z
Now,
Given that
Total bottles distributed = 879
⇒x + y + z = 879 ..............(1)
Now,
Given that, the order of bar A is half that of bar B and a quarter of bar C
⇒x = [tex]\frac{1}{2}y[/tex] , x = [tex]\frac{1}{4} z[/tex]
⇒y = 2x .............(2)
z = 4x ..............(3)
Now,
Put the values of y and z in equation (1), we get
x + 2x + 4x = 879
⇒7x = 879
⇒x = [tex]\frac{879}{7}[/tex] = 125.57
⇒y = 2(125.57) = 251.14
⇒z = 4(125.57) = 502.28
∴ we get
Total number of bottles Bar A get = x = 125.57 ≈ 126
Total number of bottles Bar B get = y = 251.14 ≈ 251
Total number of bottles Bar C get = z = 502.28 ≈ 502
hi, how can i graph the equation,
10i + 16p = t
?? thanks
Answers
Asymptotes: y=x/4, y=-x/4
Graph is inserted below :)
Which of the following pairs of equations has (5, 3) as a solution?
Answers
Answer:
the last one .
Step-by-step explanation:
like my answer and brainliest please
What is the value of the missing angle
Answers
Answer:180
Step-by-step explanation:
A pattern of ordered pairs is shown.
(0, 1), (2,4), (4,7), (6, 10)
The pattern continues. What is the eighth ordered pair in the pattern?
A. (8,13) B. (14, 18). C. (14, 22) D. (16, 19)
Answers
Answer: C
Step-by-step explanation:
X’s are going by +2 and y’s by +3
After identifying the pattern, its eighth ordered pair is: (14, 22), option C.
--------------------------
The ordered pairs given are: (0, 1), (2,4), (4,7), (6, 10)
From them, we can see that for each new ordered pair, x increases by 2, and y increases by 3.Thus, the next ordered pairs are: (8, 13), (10, 16), (12, 19), (14, 22).The eighth ordered pair is given by (14,22), option C.A similar problem is given at https://brainly.com/question/16599038
I WILL NOT ACCEPT LINKS! AND WILL REPORT!!! Please help with this geometry question. An explanation would be nice!
Answers
ON=5.099
Hope it helps
Help!!! I will give you a follow
Answers
Answer:
Red
Step-by-step explanation:
Let x = number of laps and Let y = time taken to complete laps
She is able to run one lap in 7 minutes
Given this information we want to create an equation
the equation would be
7x = y
Now that we have created an equation we want to find how many laps she can run in 56 minutes.
The time is represented by 7 so we plug in 56 into y
so now we have
7x = 56
Finally we solve for x
*divide each side by 7*
56/7 = 8
7x / 7 = x
we're left with x = 8 meaning that she can run 8 laps in 56 minutes
In conclusion the answer is the Red one
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
Complete the function table and write the function rule.
Answers
The function rule is f(x) = x - 12 and the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
Completing the function table and write the function rule.From the question, we have the following parameters that can be used in our computation:
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
The slope is calculated as
m = (2 - 20)/(14 - 32)
m = 1
So, the equation is
y = mx + c
Using the points, we have
1(32) + c = 20
Evaluate
c = -12
So, we have
f(x) = x - 12
Using the above function, we have the following function values
f(-10) = -10 - 12 = -22
x - 12 = -6
x = 6
So, the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
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Graph the equation y=5/4x - 10 using the y intercept point and slope
Answers
in order to graph this equation, you need to start off by answering the question: where is the y-intercept?
y=mx+b
m= slope
b=y-intercept
according to y=5/4x-10, our y-intercept would be -10.
now we need to find the slope, represented by m, which is 5/4.
this is where rise over run comes in.
for this problem, we rise 5 units up and run 4 units towards the right.
we can repeat these as many times as it is necessary, and also do the negative counterpart to get the rest of the line.
(5 units down, 4 units left)
hope i helped!!
slope is 5/4 and y intercept is -10 from the given equation.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation is y=5/4x - 10
In the given equation the slope is 5/4 and y intercept is -10.
to draw the graph let us find few values
x 0 1 2 3 4
y -10 -35/4 -30/4 -25/4 -5
Hence, slope is 5/4 and y intercept is -10 from the given equation.
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George decided to use blue paint to paint a wall with two windows. The wall is 12 7 8 ft by 8 ft. Both windows are 3 1 2 ft by 4 1 2 ft rectangles. Can someon egive me an answer as a whole number not a fracction Please.
Answers
Question is in picture
Answers
Answer:
casino see v
Step-by-step explanation:
j:)
29 + _ = 1000
vabbshs jsjsjsjs
Answers
Answer:
dont get it
Step-by-step explanation:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
how to do this question plz answer me step by step plzz plz please
Answers
Answer:
See the attached
Step-by-step explanation:
The solution and filled in Venn diagram is attached
A car travels at a steady speed. It covers 60km in 40 minutes. How far will it travel in 3 hours, assuming it continues at the same rate?
Answers
Answer:
270km
Step-by-step explanation:
3 hours is 180 minutes
40 minutes - 60km
180 minutes - x km
x = 180/40 * 60 = 270km (the speed is 90km/h)
solve for X
7x=49 (brainliest)
Answers
Answer:
7
Step-by-step explanation:
divide 7 to both side
7x/7=49/7
x=7
Help this is due in 2 minutes
Answers
ahhh help please find the perimeter
Answers
Answer:
12[tex]x^{2}[/tex] + 6y
Step-by-step explanation:
Help W algebra!!(logs!)
Answers
In a survey of 292 students, about 9.9% have attended more than one play. Which is closest to the number of students in the survey who have attended more than one play?
Answers
Answer:
so sorry i needed the points to ask my question.
Step-by-step explanation:
30 Students I hope it helps.
Si el precio de un artículo que es $800.000 se aumenta en su cuarta parte, y el nuevo precio se disminuye en su cuarta parte. ¿Cuál es su precio final? Explica el procedimiento
Answers
Respuesta:
$ 750 000
Explicación paso a paso:
Precio original = $ 800,000
Si el precio original se incrementa en una cuarta parte;
(800.000 + 1/4 * 800.000) = 800.000 + 200.000 = $ 1.000.000
Nuevo precio = $ 1,000,000
Si el nuevo precio se reduce en un cuarto;
1.000.000 - 1/4 (1.000.000)
1.000.000 - 250.000
= $ 750 000
El precio final es de $ 750.000