How do you know what method SSS SAS ASA AAS to use when proving triangle congruence?

Answers

Answer 1

The method to use when proving triangle congruence depends on the information given about the triangles.

What is triangle congruence?

Triangle congruence is a doctrine of mathematics which states that two triangles are congruent when all the corresponding sides and angles of both triangles have the same measure. This means that the two triangles are of the same size and shape, and each of their sides and angles correspond to each other in terms of size and measure. Triangle congruence is an important theorem in geometry, and is often used for solving various problems in mathematics.

If two triangles have three pairs of corresponding congruent sides, then the Side-Side-Side (SSS) method can be used. If two triangles have two pairs of corresponding congruent angles and a pair of corresponding congruent sides, then the Angle-Side-Angle (ASA) method can be used. If two triangles have two pairs of corresponding congruent sides and a pair of corresponding congruent angles, then the Side-Angle-Side (SAS) method can be used. If two triangles have three pairs of corresponding congruent angles, then the Angle-Angle-Side (AAS) method can be used.

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Related Questions

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include values that are undefined for tan or sin(ϴ).

Answers

Answer:

3 solutions:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is [tex]tan(\frac{\theta}{2})[/tex] so let's focus on that part of the equation first.

We know that:

[tex]tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}[/tex]

therefore:

[tex]cos(\frac{\theta}{2})\neq0[/tex]

so we need to find the angles that will make the cos function equal to zero. So we get:

[tex]cos(\frac{\theta}{2})=0[/tex]

[tex]\frac{\theta}{2}=cos^{-1}(0)[/tex]

[tex]\frac{\theta}{2}=\frac{\pi}{2}+\pi n[/tex]

or

[tex] \theta=\pi+2\pi n[/tex]

we can now start plugging values in for n:

[tex] \theta=\pi+2\pi (0)=\pi[/tex]

if we plugged any value greater than 0, we would end up with an angle that is greater than [tex]2\pi[/tex] so,  that's the only angle we cannot include in our answer set, so:

[tex]\theta\neq \pi[/tex]

having said this, we can now start solving the equation:

[tex]tan(\frac{\theta}{2})=sin(\theta)[/tex]

we can start solving this equation by using the half angle formula, such a formula tells us the following:

[tex]tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}[/tex]

so we can substitute it into our equation:

[tex]\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)[/tex]

we can now multiply both sides of the equation by [tex]sin(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=sin^{2}(\theta)[/tex]

we can use the pythagorean identity to rewrite [tex]sin^{2}(\theta)[/tex] in terms of cos:

[tex]sin^{2}(\theta)=1-cos^{2}(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=1-cos^{2}(\theta)[/tex]

we can subtract a 1 from both sides of the equation so we end up with:

[tex]-cos(\theta)=-cos^{2}(\theta)[/tex]

and we can now add [tex]cos^{2}(\theta)[/tex]

to both sides of the equation so we get:

[tex]cos^{2}(\theta)-cos(\theta)=0[/tex]

and we can solve this equation by factoring. We can factor [tex]cos(\theta)[/tex] to get:

[tex]cos(\theta)(cos(\theta)-1)=0[/tex]

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

[tex]cos(\theta)=0[/tex]

[tex]\theta=cos^{-1}(0)[/tex]

[tex]\theta={\frac{\pi}{2}, \frac{3\pi}{2}}[/tex]

Equation 2:

[tex]cos(\theta)-1=0[/tex]

we add a 1 to both sides of the equation so we get:

[tex]cos(\theta)=1[/tex]

[tex]\theta=cos^{-1}(1)[/tex]

[tex]\theta=0[/tex]

so we end up with three answers to this equation:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Answer:

its D. 3

Step-by-step explanation:

for speed runners

A number x is rounded to 1 decimal place and its 3.7
write down the error interval for x

Answers

The error is 3.65/3.74

The error interval for x would be (3.65, 3.75), indicating that the true value of x lies within this range.

Given that a number x is rounded to 1 decimal place and its 3.7.

We need to find the error of the interval for x,

To determine the error interval for the rounded number 3.7, we need to consider the possible range of values that could have been rounded to 3.7 when rounded to 1 decimal place.

When rounding to 1 decimal place, we look at the digit immediately to the right of the decimal point. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In this case, 3.7 is the rounded value, which means the original number could have been rounded up from a value greater than or equal to 3.65 or rounded down from a value less than 3.75.

Therefore, the error interval for x would be (3.65, 3.75).

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This app is so bad nowadays. No one answers your questions and if they do they respond with useless links...

Answers

Answer:

I know. It's a pain. I just put tons of points on and that seems to attract people.

Step-by-step explanation:

A group of people are fundraising, and each person raises a certain amount of money for every mile they walk. Each person's fundraising is
represented below using d for the dollars that person raises and w for the miles that person walks

Answers

Answer:

lk

Step-by-step explanation:

on

Marcos and his sister Yvette record their age each year in an annual scrapbook.
The table below shows their recorded ages for the past three years.
Which equation correctly shows the relationship between Marcos's age, m, and
Yvette's age, y?
Marcos
Yvette
10
4
11
5
12
6
4 O y = 7
O y = m + 6
O y = 6m
O y = m - 6

Answers

Answer:

It’s b

Step-by-step explanation:

Just think

I need help on this question (^~^;)ゞ​

Answers

Answer:

which part bro I need to know at least

What is the question

Quinn is a contestant on a quiz show. Quinn's score changes by -15 points for 4 questions in a row. ) What is the total change in Quinn's score?​

Answers

Answer: Quinn is a contestant on a quiz show. Quinn's score changes by -15 points for 4 questions in a row. ) What is the total change in Quinn's score?

hope this help :}


HELLLPPP!!!
What is the equation of the parabola with focus(1, 1/2)
and directrix y = 3?
A. Y=x^2+17x-1
B. Y=-3/16x^2
C. Y=1/5x^2+2/5x+31/20
D. Y=-3/5x^2-14/31x+71/16


Answers

Given:

Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]

Directrix: [tex]y=3[/tex]

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex]            ...(A)

Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.

On comparing the focus, we get

[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]

[tex]h=1[/tex]

[tex]k+a=\dfrac{1}{2}[/tex]           ...(i)

On comparing the directrix, we get

[tex]k-a=3[/tex]              ...(ii)

Adding (i) and (ii), we get

[tex]2k=\dfrac{7}{2}[/tex]

[tex]k=\dfrac{7}{4}[/tex]

Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get

[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]

[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]

[tex]a=\dfrac{-5}{4}[/tex]

Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get

[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]

[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]

[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]

On further simplification, we get

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]

Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].

Note: Option C is correct but the leading coefficient should be negative.

Solve for the given variable in the equation: ½ n - 3 = 5

n = _______

Answers

Answer:

The correct solution is "n = 16".

Step-by-step explanation:

The given equation is:

⇒  [tex]\frac{1}{2} n-3=5[/tex]

On adding "3" both sides, we get

⇒  [tex]\frac{1}{2} n-3+3=5+3[/tex]

⇒  [tex]\frac{1}{2}n=8[/tex]

On applying cross multiplication, we get

⇒  [tex]n=8\times 2[/tex]

⇒  [tex]n=16[/tex]

Help please due today!!

Answers

In this image, the two angles (equations) form a right angle, which is 90°. You combine these equations: 4y-7+3y-1. When you combine like terms, you get 7y-8. You set this equal to 90°. 7y-8=90. Solve for y, and you get y=12.

Based on the figure, which of the following equations is also true?
с
A sin 38°
17
17
B cos 38°
с
17
cos 52°
с
с
D tan 52°
17

Answers

Answer:

The correct answer is B.

Step-by-step explanation:

Because you know two of the angles in a triangle are 90° and 52°, you can infer that the third angle is 38°. There is a trigonometry rule that states the sine of an angle is equivalent to the cosine of 90° minus that angle, which you can apply to here. Since [tex]Sin(52[/tex]°[tex])[/tex] = [tex]\frac{17}{c}[/tex], you know that [tex]Cos(90[/tex]°[tex]-52[/tex]°[tex])[/tex] or [tex]Cos(38[/tex]°[tex])[/tex]also equals [tex]\frac{17}{c}[/tex], so choice B is the correct answer.

Θ lies in quadrant III, φ lies in quadrant I. cos θ = -8 /17 , cos φ = 15 /17 . What is cos (θ - φ)?

Answers

Answer:

cos(θ - φ) is -240/289

Step-by-step explanation:

The given parameters are;

The location of θ = Quadrant III

The location of φ = Quadrant I

cos(θ) = -8/17

cos(φ) = 15/17

By trigonometric identities, we have;

cos(θ - φ) = cos(θ)·cos(φ) - sin(θ)·sin(φ)

Given that 'θ' is in quadrant III, we have;

sin(θ) is negative

By Pythagoras' theorem, we have;

∴ sin(θ) = -√(17²- 8²)/17 = -15/17

Whereby 'φ' is in quadrant I, by Pythagoras' theorem, we have;

sin(φ) = √(17² - 15²)/17 = 8/17

∴ cos(θ - φ) = (-8/17) × (15/17) + (-15/17) × (8/17) = -240/289 = -0.83044982699

a jug holds 2 cups of liquid. a recipe for fruit punch is 1/2 cups of orange juice. 1/4 cup of raspberry juice, 3/8 cups of grapefruit juice, and 5/8 cups of lemonade. the the jug big enough for the punch? explain

Answers

Yes the jug can hold the punch!

If you add up 1/2 + 1/4 + 3/8 + 5/8 you’ll end up with 1 and 3/4 cup so it is close to 2 cups but not quite there yet!

Hope this helps!

PLEASE HELP ASAP AND PLS HURRY NO LINKS
Samantha and her children went into a grocery store and she bought $7 worth of bananas and peaches. Each banana costs $0.40 and each peach costs $0.50. She bought a total of 15 bananas and peaches altogether. Determine the number of bananas and the number of peaches that Samantha bought.

Answers

Answer: 10 peaches and 5 bananas

Step-by-step explanation:

To solve the problem increase the cost by adding more peaches and less by adding more bananas

7 peaches = 3.50

8 bananas = 3.20 + 3.50 = 6.70

We need 30 more cents so add three more peaches

10 peaches = 5

5 x 0.4 = 2

2 + 5 = 7

the sum of 2 times a number and 4 equals 3
HELP ASAP

Answers

Answer:

The number is - ½

Step-by-step explanation:

Let the missing number be x

2x + 4 = 3

2x = 3 - 4

2x = - 1

x = - ½

Answer:

-1/2

Step-by-step explanation:

you have to make it like this and use a variable:

2x+4=3

take away 4 from both sides:

2x= -1

divide by 2:

x = -1/2

Solve x/3 = 9.
anyone wanna help lol?

Answers

Answer:

x=27

Step-by-step explanation:

Answer:

The answer would be 27

Step-by-step explanation:

Times three by nine to get the value of x.

Type equation for the line shown in the graph

Answers

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 5) ← 2 points on the line

m = [tex]\frac{5-3}{2+2}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 5 ) , then

5 = 1 + c ⇒ c = 5 - 1 = 4

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Which is the opposite of -5?

Answers

Answer: 5

Step-by-step explanation: 5*-1=-5

A shipping container is in the shape of a right rectangular prism with a length of 5 feet, a width of 12.5 feet, and a height of 14 feet. The container is completely filled with contents that weigh, on average, 0.78 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?

Answers

Answer:

102 pounds

Step-by-step explanation:

Volume of Right rectangular prism = 12 * 8.5 * 4  = 408 cubic feet

Density = Mass / Volume

=>  0.25  = Weight of contents in container / Volume of container

=> 0.25 = Weight of contents in container / 408

=> Weight of contents in container  = 0.25 * 408

=> Weight of contents in container  = 102 pounds

Answer:

683lb

Step-by-step explanation:

The circle shown has a radius of 4 cm.
Not drawn
to scale
Х
What is the length of the diameter of the circle?

Answers

Answer:

8 cm

Step-by-step explanation:

:)

8 cm. Because the diameter is the the radius times 2

HALPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP. Please no links :P

Answers

Answer:

it will be x < 2

Step-by-step explanation:

Because the circle means greater than or less than. And if the circle isn't fillied up it means it is greater than or equal to or less thanor equal to.

True. For sure that is the answer

IM SO TIRED CAN SUM1 HELP PLS.

Answers

Answer:

a. $250

b. 50x + 200

Step-by-step explanation:

a. For the first month, you have to account for the cost to start which is $200, and the adition of the $50 for each month.

b. the 200 is only a one time fee so you add it on to months(x)

Answer:

a. 250$

b. 200+50x

Step-by-step explanation:

#1 What is the total cost to use the cell phone plan for one month?

GIVEN:

Startup price=$200

Charge per month=50$

SOLVE:

The total cost for one month will be the startup price+ charging price for one month.

200+50=250$

#2 What is the total cost for x months?

The total cost for x months will be the startup price+charging price for x months.

200+50x

Hope this helps!! :)

Please let me know if you have any questions

The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who
give birth in the next year. Which is the best description of the shape for the sampling distribution of ?
skewed left
skewed right
uniformly distributed
approximately Normal

Answers

Answer:

D: Approximately Normal

Step-by-step explanation:

I got it right on edg.

(8,1), (-2,-5) midepoint

Answers

Answer:

(3, -2)

Step-by-step explanation:

The x-coordinate of the midpoint of the line segment connecting (8, 1) and (-2, -5) is -2 plus half the horizontal distance from -2 to 8, which is 10, or 5.  We add 5 to -2, obtaining 3 units.

The y-coordinate of the midpoint is found similarly.  The vertical distance between the two given points is 1 - (-5), or 6 units.  Half of that is 3 units.  Adding 3 units to -5 yields -2.

The midpoint is (3, -2).

Thus, the coordinates of the midpoint at (-7, 6)

product of 2 and the difference between t and 1 is 14 ​

Answers

Answer:

2x + t - 1 =14

Step-by-step explanation:

give me brainliest plz and hope this helps also i am very good at math so that is a reassurance that this is correct

In ΔFGH, the measure of ∠H=90°, the measure of ∠F=44°, and GH = 14 feet. Find the length of HF to the nearest tenth of a foot.

Answers

Answer: 14.5 feet

Step-by-step explanation: that’s he correct answer delta math gave me AFTER I got it wrong

Answer:

14.5

Step-by-step explanation:

Help me grade 9! Thankyou

Answers

Answer:

got ya

Step-by-step explanation:

Laurence is saving money for a set of speakers. He has $230 dollars in his savings right now. He just got a part-time job at Kroger and can increase his savings account by 20.6% each week. Write an equation to represent the amount of money
in his account, y after x weeks.

Answers

It shall be 230(1.206)^x=y

The length of a rectangle is the sum of the width and 1. The area of the rectangle is 20
units. What is the width, in units, of the rectangle?

Answers

Answer:

4 units

Step-by-step explanation:

Create an equation where w is the width of the rectangle

Use the area formula, A = lw.

Since the length is the sum of the width and 1, it can be represented by w + 1

Plug in this and the area into the formula, and solve for w

A = lw

20 = (w + 1)(w)

20 = w² + w

w² + w - 20

(w + 5)(w - 4)

Solve for w:

w + 5 = 0

w = -5

w - 4 = 0

w = 4

Since the width cannot be negative, the answer must be 4.

So, the width of the rectangle is 4 units.

Answer:

Solution :-

We know that

Area = Length × Width

Area = w + 1 × w

Area = w² + w

w² + w - 20

w² + (5w - 4w) - 20

(w + 5)(w - 4)

Either

w = -5

or w = 4

Breadth can't be negative

So,

Breadth = 4 units

how do you get from 1/12 to 2/3? please hurry, i am confused

Answers

Answer:

to get to 2/3 from 1/12, add 7/12 to 1/12.

Step-by-step explanation:

8/12 is equivalent to 2/3

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