Create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem.
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For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
How can the distance formula prove SSS Triangle Congruence Theorem?Given that the distance formula =
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
Let say that Angle ABC has the vertices of A (-4, -2), B (-5,1). C (0,2) and Angle DEF has the vertices of D (7, -4), E (4,-5), F (3,0)
So lets prove it:
AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Do the same for DF:
DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.
Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
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Related Questions
Pls pls pls pls help
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Step-by-step explanation:
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.
A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.
It is then easy to show that the triangles ΔAOD and ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.
And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
PROOF
(1) ABCD is a rhombus //Given
(2) AB=AD //definition of rhombus
(3) AO=AO //Common side, reflexive property of equality
(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other
(5) △AOD≅△AOB //Side-Side-Side postulate.
(6) ∠AOD ≅ ∠AOB //Corresponding angles in congruent triangles (CPCTC)
(7) AC⊥DB //Linear Pair Perpendicular Theorem
The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.
What is the domain of all of these points?
(8, 2), (12,9), (16, 16), (20, 23)
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Answer:
8, 12, 16, 20
Step-by-step explanation:
those are the domains
(−3⋅10^3 )⋅(4⋅10^6)=???
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Answer:
-1.19164 x 10^8
Step-by-step explanation:
Select all that apply. Select the formulas that give the amount P in the account after the first period.
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Options :
a.) P=1.005Po
b.) P=1.02Po
c.) P=Po(0.02/4)
d.) P=Po(4.02/4)
e.) P=Po(1+ 0.02/4)
Answer:
a.) P=1.005Po
d.) e.) P=Po(1+ 0.02/4)
Step-by-step explanation:
From the compound interest formula:
P = P0(1 + r/n)^t
Rate = 2% = 2/100 = 0.02
n = Number of compounding times per period, quarterly ; n = (12 /3) months
P = P0(1 + 0.02/4)^1
P = p0(1 + 0.02/4)
Simplifying further :
P = P0(1 + 0.005)
P = p0(1.005)
Plz help me! I need an answer right away
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How many solutions does this system of equations have?
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Answer:
One solution.
A system of linear equations has one solution when the graphs intersect at a point.
I hope it's helpful!
The tree frog population in your back yard doubles every two weeks. Currently, there are 10 frogs in your back yard. Assuning that there are 4
weeks in a month how many tree frogs will there be in 3 months?
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Answer:
there would be 40,960 tree frogs i think
Step-by-step explanation:
Answer:
640 tree frogs
Step-by-step explanation:
If 1 month = 4 weeks
3 months = 12 weeks (3x4)
After 2 weeks the frogs double to 20
After 4 weeks the frogs double to 40
6 weeks, it doubles to 80
8 weeks, it's 160
10 weeks it's 320
12 weeks, it's 640
Which of the following nets is for a pyramid?
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2nd one
hope it helps you
The net of the pyramid is given by figure B
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
A net is a two-dimensional representation of a three-dimensional shape that, when folded along the edges, forms the shape of the solid.
In the case of a pyramid, the net consists of a polygonal base and triangular faces that meet at a common vertex.
The number of triangular faces depends on the type of pyramid (triangular, square, pentagonal, etc.).
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f(x) = -3x + 3
f(-2) = [?]
Help
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is this the answer you're looking for? I'm sorry I'm confused
please helppppppp
give u 10 pts
Answers
Answer:
y = x / -4
Step-by-step explanation:
Hope that helps!
Help fast please. I will give brainliest.
Answers
Answer:
Q5 ) A 80 UNITS²
pls give me brainliest
An account earns simple interest.
$1500 at 4% for 5 years
a. Find the interest earned.
$
b. Find the balance of the account.
Answers
Answer:
a) $300 in interest
b) $1800 account total
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 1500(.04)(5)
I = 300
A = P + I
1800 = 1500 + 300
what r passing marks out of 40
Answers
Answer:
36/40 - A, 32/40 - B, 28/40 - C, and 24/40 - D
Step-by-step explanation:
Answer:
18 is ur answer
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and please explain it so I won't get confused further on
Answers
Now, to find m<7
A straight line is 180 degrees. One side is already given. m<8+m<7 = 180 degrees. So 180-110=70.
Answers:
4. m<7= 70 degrees
5. m<8= 110 degrees
What number is 40% of 15? Round to the nearest hundredth
Answers
Answer:
6Step-by-step explanation:
10% of 15 = 1.5x4=612 (X + 2) - 4x = 4( 2X + 11 ) -20
Solve for X
Answers
Answer:
Step-by-step explanation:
12 (x + 2) - 4x = 4 (2x + 11) - 20
12 + 24 - 4x = 8x + 44 - 20
36 - 4x = 8x + 24
36 - 24 = 8x - 4x
12 = 4x
---- ----
4 4
3 = x
-x = -3
x = 3
Can someone help w/ this math problem plzz
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Answer:
its C
Step-by-step explanation:
what is the decimal word form of 120.95?
Answers
4k squared = 100 solve for k
Answers
Answer:
k = 5
Step-by-step explanation:
4k^2 = 100
4k^2/4 = 100/4
k^2 = 25
k=5
pls help me it is inportant
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Answer:
(5.x)+(5.2)
Step-by-step explanation:
Hope it helps you......
Answer:
nah
Step-by-step explanation:
Please Help! Ill give brainliest no fakes PLEASE!!
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Answer:
4 and then 15
Step-by-step explanation:
second one: 6:4
last one: 15:10
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Answer:
split then d the trinangle with the base and the height and do the rectangle as length times width
Step-by-step explanation:
Answer: 1152
Step-by-step explanation:
Find the ratio of 580 ml to 1.12 I to 104 ml
Answers
Answer:
580 : 1120 : 104
Step-by-step explanation:
1.12 ml -> 1120 ml
hence,
580 : 1120 : 104
6 tubs hold 125 gallons in all how much does each run hold
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Answer:
125/6= 20.8 gallons
FIND THE DOMAIN AND RANGE!!!!
Answers
I need help it's geometry
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Step-by-step explanation:
[tex] \sin(45) = \frac{x}{5} \\ \frac{1}{ \sqrt{2} } = \frac{x}{5} \\ x = \frac{5}{ \sqrt{2} } = 3.535[/tex]
[tex] \sin(45) = \frac{y}{5} \\ y = \frac{5}{ \sqrt{2} } = 3.535[/tex]
Answer:
[tex]\frac{5\sqrt{2} }{2 }[/tex]
Step-by-step explanation:
x=y
45-45-90 equation is x-x- x square root of 2
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Sin(40)=x/19
*19 *19
12.2129=x
If the mean of 5 numbers is 10 and the mean of other 15 numbers is 20 , what is the combined mean of both 20 numbers
Answers
9514 1404 393
Answer:
17.5
Step-by-step explanation:
The sum of the 5 numbers is 5·10 = 50.
The sum of the 15 numbers is 15·20 = 300.
The sum of all 20 numbers is then 50+300 = 350, so their mean is ...
mean = sum/number = 350/20 = 17.5
The combined mean of the 20 numbers is 17.5.
HELP I NEED HELP ASAP
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Answer:
C
Step-by-step explanation:
Answer:
exponential;increase
Step-by-step explanation:
answer is C
solve the equation 3(x + 1) + 6 = 33.
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Answer:
155
Step-by-step explanation: