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.

Learn more about congruent Angle from

https://brainly.com/question/2938476

#SPJ

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.

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:

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

(−3⋅10^3 )⋅(4⋅10^6)=???

Answers

Answer:

-1.19164 x 10^8

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

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

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

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

Answers

Answer:

155

Step-by-step explanation:

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

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 is the decimal word form of 120.95?

Answers

One hundred twenty and ninety-five hundredths ?

One hundred and twenty point nine five

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!

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.).

To learn more about surface area of pyramid click :

https://brainly.com/question/15050758

#SPJ2

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 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

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

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!

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

Answers

Answer:

125/6= 20.8 gallons

HELP I NEED HELP ASAP

Answers

Answer:

Step-by-step explanation:

Answer:

exponential;increase

Step-by-step explanation:

answer is C

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

Help fast please. I will give brainliest.

Answers

Answer:

Q5 ) A 80 UNITS²

pls give me brainliest

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

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

Answers

Answer:

Step-by-step explanation:

10% of 15 = 1.5x4=6

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:

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.

Plz help me! I need an answer right away

Answers

The answer is G ( 1/9 )

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

Answers

is this the answer you're looking for? I'm sorry I'm confused

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)

Can someone help w/ this math problem plzz

Answers

Answer:

its C

Step-by-step explanation:

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

Other Questions

Match the question with the evaluation criteria.a. Coverage or Relevanceb. Author or Authority c. Objectivity or Bias d. Currency e. Accuracy or Credibilityf. Sources or Documentation 1. Is the information provided based on proven facts? 2. Does the information covered meet your information needs? 3. Is there a political, social or commercial agenda? 4. What is the author's area of expertise? 5. When was the Web site last updated? 6. Is there information provided to support statements of fact? > Ruthie is trying to choose what reading material she wants to take on a vacation. She wants to read 1 fiction book, 1 nonfiction book, and 3 magazines. If Ruthie has 8 fiction books, 7 nonfiction books, and 3 magazines to choose from, how many possible combinations of books and magazines could she take with her.E. 3 F.8 G.56 H.112 n which type of linear perspective does an artist generate complete views by using lines that converge horizontally, as well as vertically What in joseph smith's wentworth letter might offend non-mormon americans? Conjugate the verb in parentheses for the subject of each sentence.(HIGH SCHOOL SPANISH) 35. what represents the structure of kelp from top to bottom? -holdfast, blade gas bladder -blade, gas bladder, holdfast -stipe, holdfast, blade -gas bladder, holdfast, stipe Which cast care instructions should the nurse provide to a client who has just had a plaster cast applied to the right forearm In a zoo, the ratio of female to male tiger is 2:3.There are 30 male tigers.How many tigers are female? A rigid, nonconducting tank with a volume of 4 m3 is divided into two unequal parts by a thin membrane. One side of the membrane, representing 1/3 of the tank, contains nitrogen gas at 6 bar and 100oC, and the other side, representing 2/3 of the tank, is evacuated. The membrane is ruptured and the gas fills the tank. (a) What is the final temperature of the gas? How much work is done? Is the process reversible? (b) How much work is done if the gas is returned to its original state by a reversible process? Assume nitrogen ideal gas for which Cp = (7/2) R and Cv = (5/2)R. Cual es parte de un crucero? Brittany and four of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than eighteen players. In interval notation, how many more people can join Brittany's team? 12. Change into passive. [5] i) He likes coffee. ii) My parents, cared me a lot. iii) Someone was knocking the door.. iv) She will call you after 5 P.M. v) The police have found the criminal. Jace ordered a banner in the shape of a parallelogram from a print shop.A parallelogram is shown. The length of the sides are 9 feet, and the length of the top and bottom sides are 12 feet. A diagonal is drawn from one point to the opposite side. The length of the diagonal is 19 feet.Herons formula: Area = StartRoot s (s minus a) (s minus b) (s minus c) EndRootThe print shop charges $1.10 per square foot for banners of any shape and size. What is the approximate cost of the banner before tax?$41.95$46.14$83.90$92.30 President nixons managerial style was mostly known for being _____ of outsiders. Rates of alcoholism among asian populations are __________ than among european peoples. this fact may be related to __________. A group of 100 parents who were abused as children have gathered at a conference to discuss challenges of raising a family. About how many of the group have abused their own children? Select ALL the correct answers. What two factors led to the US being considered a powerful nation during World War I After abdominal surgery, a client with protein calorie malnutrition is receiving parenteral nutrition (PN). Which is the best indicator that the client is receiving adequate nutrition point(s) possibleSet up a ratio for the following information and reduce to lowest terms: $3 per day for 12 employees for 39 days. A ________ can educate customers when discussing their products or services and create excitement when they promote special offers.