Create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem.

Answers

Answer 1

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

Answers

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.

Plz help me! I need an answer right away

Answers

The answer is G ( 1/9 )

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.

solve the equation 3(x + 1) + 6 = 33.

Answers

Answer:

155

Step-by-step explanation:

Help fast please. I will give brainliest.

Answers

Answer:

Q5 ) A 80 UNITS²

pls give me brainliest

I need help it's geometry

Answers

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

pls help me it is inportant

Answers

Answer:

(5.x)+(5.2)

Step-by-step explanation:

Hope it helps you......

Answer:

nah

Step-by-step explanation:

6 tubs hold 125 gallons in all how much does each run hold

Answers

Answer:

125/6= 20.8 gallons

What is the domain of all of these points?
(8, 2), (12,9), (16, 16), (20, 23)

Answers

Answer:

8, 12, 16, 20

Step-by-step explanation:

those are the domains

How many solutions does this system of equations have?

Answers

Answer:

One solution.

A system of linear equations has one solution when the graphs intersect at a point.

I hope it's helpful!

Can someone help w/ this math problem plzz

Answers

Answer:

its C

Step-by-step explanation:

f(x) = -3x + 3
f(-2) = [?]
Help

Answers

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!

Use desmos calculator graphing. Tap the plus. Tap table. Enter x1 on one side and y1 on the other. Enter the data for each side. Make a new equation and Use the following formula: y~ab^x1 = y=0.18(0.74)^x

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

HELP I NEED HELP ASAP

Answers

Answer:

Step-by-step explanation:

Answer:

exponential;increase

Step-by-step explanation:

answer is C

what is the decimal word form of 120.95?

Answers

One hundred twenty and ninety-five hundredths ?

One hundred and twenty point nine five

Which of the following nets is for a pyramid?

Answers

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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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

thank you

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

SOMEONE PLEASE HELP

and please explain it so I won't get confused further on

Answers

Number 5 is 110 degrees because it is the same angle as m<2.

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

12 (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

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

(−3⋅10^3 )⋅(4⋅10^6)=???

Answers

Answer:

-1.19164 x 10^8

Step-by-step explanation:

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?

Answers

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

Select all that apply. Select the formulas that give the amount P in the account after the first period.

Answers

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)

is the answer 84.2??? if not pls explain THANK U ITS GEOMETRY

Answers

The answer is 12.2129

Sin(40)=x/19
*19 *19
12.2129=x

Please Help! Ill give brainliest no fakes PLEASE!!

Answers

Answer:

4 and then 15

Step-by-step explanation:

second one: 6:4

last one: 15:10

Help Please................

Answers

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 DOMAIN AND RANGE!!!!

Answers

For the domain, you would find that all the numbers that go across in the x axis. In this case -3 is less than or equal to x which is less than or equal to 4. Same with the range, different numbers. -3 is less than or equal to y which is less than or equal to 2. Hope this helped!

What number is 40% of 15? Round to the nearest hundredth

Answers

Answer:

Step-by-step explanation:

10% of 15 = 1.5x4=6

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