Is AAS and ASA congruence are same?

Answers

Answer 1

No, AAS ( Angle , Angle , Side) congruence postulate is not same as ASA (Angle, Side, Angle) congruence postulate, because in AAS consists one equal side between both triangles either it PR = AC or PQ = AB . But ASA must include side equality in this case i.e BC = QR and both are not same.

Two triangles are said to be congruent if they have all three same angles as well as same sides. AAS and ASA are basic methods through which we can prove that two triangles are congruent. So, to check that wheather both methods are same we will take one example of two triangles. So, consider two triangles, ∆ABC and ∆PQR as seen above in figure, ∠ ABC = ∠ PQR = 40° and ∠ACB = ∠ PRQ = 80° and AC = QR

According to AAS rule, if two pairs of corresponding angles with opposite or non- including side is same and the equality in opposite sides are equal to each other then the triangles are congruent. We have ,

∠ PRQ = ∠ ACB , ∠ABC = ∠PQR

and either PR = AC or PQ = AB.

if the above three conditions are satisfied then ∆ABC congruent to ∆PQR.

According to ASA rule , if two angles of one triangle with one side contained between two angles are respectively equal to two angles of another triangle and one side contained between them , then triangles are congruent. We have, ∠ R =∠C , ∠B = ∠Q and BC = QR

if the above three conditions are satisfied then both triangles are congruent. As we see clearly both congruence postulates are not same.

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Is AAS And ASA Congruence Are Same?

Related Questions

X-9/2=12
X=?
Find what does x equal to.

Answers

Answer:

x = 33

Step-by-step explanation:

cross-multiply:

x-9 = 2(12)

x-9 = 24

x = 33

Answer:

The answer is 33.

Step-by-step explanation:

1) Multiply both sides by 2.

[tex]x - 9 = 12 \times 2[/tex]

2) Simplify 12 × 2 to 24.

[tex]x - 9 = 24[/tex]

3) Add 9 to both sides.

[tex]x = 24 + 9[/tex]

4) Simplify 24 + 9 to 33.

[tex]x = 33[/tex]

Hence, the answer is 33.

make x the subject of the formula y=2x+4

Answers

Answer:

X= y/2-2

Step-by-step explanation:

Well to isoalte x just do the same thing you would do for y,

Isolate the numbers without a variable buy subtravting 4 on each side.

y-4=2x

Now isolate 2 and x by divide 2 on both sides

y/2-2=x

This can be determined by the simple mathematical concepts.  Therefore the value of x is,  [tex]\bold{x=\dfrac{y-4}{2} }[/tex]   the subject of he formula y=2x+4.

Given that the subject of the formula y=2x+4.

We have to find x.

According to the question,

To obtained the value of x by the  given formula

i.e.  y = 2x+4                   .....(1)

Now the value of x is from the above equation (1)...

[tex]\bold{x=\dfrac{y-4}{2} }[/tex]

Hence, the value of x ,  [tex]\bold{x=\dfrac{y-4}{2} }[/tex]    makes x the subject of the formula y=2x+4.        

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Find (3c2 - 8c + 5) + (c2 - 8c - 6).
A
3c2 - 1

B
4c2 - 16c - 1

C
2c2 - 16c - 1

Answers

Answer: B

4c^2 - 16c - 1

Step-by-step explanation:

(3c2 - 8c + 5) + (c2 - 8c - 6).

remove parantheses.

3c2 - 8c + 5 + c2 - 8c - 6

add common factors

answer= 4c^2 - 16c - 1

please help!!!!



polygon MNOPQ is dilated by a scale factor of 5.4 with point M as the center of dilation to form the image M’N’O’P’Q’. compare NO and N’O’. N’O’ ____ through point M. the slopes of N’O’ and NO are ____



the first blank answer choices are: passes, or does not pass

the second blank answer choices are: the same, or different

Answers

Right I needed help on this

The ages of the members of the Chess Club and the Debate Team at Jana’s school are shown in the box plots. Which statement is true regarding these data sets?

Answers

Answer:

C lul

Step-by-step explanation:

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(The majority of the members in each club are between 15 and 17 years old.)

C lol lol I need points I’m so sorry

What is the center of the circle and radius defined by the following equation?

x2+y2+4y=5

Answers

Answer:

Step-by-step explanation:

Alternate forms:

x^2 + y (y + 4) = 5

x^2 + y^2 + 4 y - 5 = 0

Solutions:

y = -sqrt(9 - x^2) - 2

y = sqrt(9 - x^2) - 2

Integer solutions:

x = ± 3, y = -2

x = 0, y = -5

x = 0, y = 1

Implicit derivatives:

(dx(y))/(dy) = -(2 + y)/x

(dy(x))/(dx) = -x/(2 + y)

1. What is the minimum value of y in the graph below
y

Answers

Answer:

-1

Step-by-step explanation:

Solve for x! , Please answer!!
If you can please show the explanation <3
Have a good day!

Answers

Answer:

Value of x = -7

Step-by-step explanation:

Given:

First angle = 83°

Second angle = 24°

Third angle = (38 - 5x)°

Find:

Value of x

Computation:

We know that sum of all interior angle in triangle is 180°

So,

83 + 24 + 38 - 5x = 180

145 - 5x = 180

-5x = 35

x =  -7

Value of x = -7

Sam has worn a green shirt on 10 of the last 20 days. Considering this data, how many times
would you expect Sam to wear a green shirt in the next 12 days?

Answer quickly

Answers

I think it is 6 because 10 is half of 20 so 6 is half of 12

Sam should wear green shirt for 6 days in next 12 days.

What is fraction?

Fraction is a number that represent part of a whole quantity. It has two parts, numerator and denominator, the number above the horizontal line is numerator, and number under the the line is denominator.

Given,

Sam wore green shirt on 10 of the last 20 days

Fraction of days the wearing green shirt to total days = 10/20 = 1/2

Number of days of wearing green shirt in next 12 days

= 12 × 1/2

= 6 days

Hence, in next 12 days, Sam should wear green shirt for 6 days.

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May someone please help me with this :)

Answers

Answer:

i was taught this but i dont remember so I dont know if I can help sorry bud

Write the equation that describes the following variation. Don't forget "k"!
x varies directly with the square rootſofy and inversely with the square of w and the
cube root of z

Answers

Answer:

x=(k√x)/(w^2)(cube√z)

x varies directly with square root of y is:

x = k √y

And inversely with the square of w and cube root of s is:

/(w^2)(cube√z)

Now put those together:

x=(k√x)/(w^2)(cube√z)

The formula is:

x=ky/wz but add the specific info like square, roots, or etc

omg I need help w all the questions lol someone pls help me. If u can message me and tell me or help me w the answers

Answers

What’s the height?
Formula is: V= πr2h
d=4 in
r=2 in
V= π•2^2•h
V= π•4•h
If h is 3, answer is B. If h is 9, answer is C. Good luck.

Classify the polynomial by degree and number of terms.
-2x² + x4 +3
constant
linear
quadratic
cubic
quartic
monomial
binomial
trinomial

Answers

Answer:

linear

Step-by-step explanation:

Answer: its a trinomial

Step-by-step explanation:

Substitution
x+5y=13, 4x+7y=0
PLEASE HELP MEE<3


Answers

Step-by-step explanation:

x+5Y=13...... 1

4x +7y=0..... 2

from eqn 1

x =13-5y

substitute into eqn 2

[tex]4(13 - 5y) + 7y = 0[/tex]

52-20y +7y=0

52-13y=0

52=13y

y=52÷13

y=4

substitute Y into eqn 2

x +5y=13

x + 5(4)= 13

x+ 20=13

x=13-20

x=-7

HELP WITH THESE QUESTIONS ILL GIVE OUT BRAINLEST

Answers

Answer:

#3 is b

#4 is also b

Step-by-step explanation:

A blade of a windmill completes 1 rotation every 4 seconds. The outer end of the blade travels 600 feet in 1 rotation. What is the speed of the outer end of the blade in feet per minute?

NEED ANSWERS ASAP

Answers

Answer:

900 feet per minute

Step by step solution:

I did 60÷4 then it is 15 so 600*15 is 9000

Hope i am right...

What is the slope of y = -x + 7?

Answers

Answer:

The slope is -1

Step-by-step explanation:

The slope is always the number in front of the x.

PPPPPPPPPPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP I NEED ALL 3 QUESTIONS ANSWERED

Answers

The image is blank for me

HELPPP ROUND TO THE NEAREST TENTH

Answers

8293 haha the owl and I will be in the

A CD usually sells for $18.00. If the CD is 10% off, and sales tax is 7%, what is the total price of the CD, including tax?
A. $18.30
B. $17.33
C. $17.46
D. $17.50

Answers

Answer:

b

Step-by-step explanation:

The weight limit for suitcase is 23 kg. You want to make sure that you will not be charged baggage fees on your flight back. What is the weight limit in pounds? 1 kg = 2.2 pounds.

Answers

Answer:

33lbs

Step-by-step explanation:

Write an equation of the line that passes through the points (-2,-7) and (0,-4). ​

Answers

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

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

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] ) point - slope form of a line.

y = mx + b slope- intercept form of a line.

~~~~~~~~~~~~~~~~~

( - 2, - 7 )

( 0, - 4 )

m = [tex]\frac{- 4 - (-7)}{0 - (- 2)}[/tex] = [tex]\frac{3}{2}[/tex]

y - ( - 4 ) = [tex]\frac{3}{2}[/tex] ( x - 0 )

y + 4 = [tex]\frac{3}{2}[/tex] x

y = [tex]\frac{3}{2}[/tex] x - 4 slope- intercept form

3x - 2y = 8 standard form

Find the cardinal number of the indicated set. Use the cardinal number formula.
F4) If n(A) - 10, n(
AB) = 28, and n(AB) = 6, find n(B).
A) 24
B) 18
C) 25
D) 23
Find the cardinal number

Answers

Answer is D.) 23 hope I could help;) tjrjdfjfjfnf f f find zo d d
Dkixkckckcmcxnxmxmxmd

PLEASE HELP FOR MATH!!!!

Answers

345 I think if it’s wrong I’m sorry

230 Just add and divide

I need help with some scientific notation problems

Answers

Answer:

1) 4.5 x 10^3 =4,500

2)5.78 x 10^-2

3) 5.7 x 10^1 = 57

4) 6.256 x 10^-3 = 0.006256

5) 7.3 x 10^2 = 730

6) 4.2 x 10^-5 = 0.000042

7) 7x10^-3 = 0.007

8) 2.563 x 10^1

9) 3.0025 x 10^2 = 300.25

10) 1.456 x 10^-1

The diameter from the outer edge of the rubber of my old tires to the center of the tire is 76cm (30inches). What is the circumference of the tires?

Answers

Answer:

The circumference of the tires is of 94.25 inches.

Step-by-step explanation:

Circumference of a circle:

The circumference of a circle, with radius measuring r, is given by:

[tex]C = 2\pi r[/tex]

In which the radius is half the diameter.

In this question:

Diameter of 30 inches, so the radius is 30/2 = 15 inches.

The circumference is:

[tex]C = 2\pi (15) = 30\pi = 94.25[/tex]

The circumference of the tires is of 94.25 inches.

Classify the graph.
A?
B?
C?
D?

Answers

Answer:

linear

Step-by-step explanation:

you can tell its linear bc its in a straight line

hope this helps <3

the following question statistical? Explain. How do shoppers in a town pay for their groceries? Choose the correct answer below. A. Yes , it is statistical . More than one response is possible . B. No , it is not statistical . Only one response is possible . C. Yes , it is statistical . Only one response is possible . D. No, it is not statistical. More than one response is possible .

Answers

Answer:

A grocery store is interested in how much money, on average, their customers spend each visit in the produce department. Using their store records, they draw a sample of 1,000 visits ...

Yes , it is statistical. More than one response is possible .

What is statistics?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, and presentation of large amounts of data. It involves the use of data to make decisions and predictions based on probability and uncertainty. Statistics is used in a wide range of fields, from medicine and social sciences to business and engineering.

This question is asking for a statistical response because it is seeking information about the ways in which shoppers in a town pay for their groceries. The answer can vary from person to person, so there are multiple possible responses, making it a statistical question.

Therefore, option C is the correct answer.

Learn more about the statistical data here:

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There is 13 gallons of water in a 3-gallon container. What fraction of the container is filled? 1. Write a multiplication equation and a division equation to represent the situation. Use "?" to represent the unknown quantity. Do not use parentheses in either of the equations.

Answers

Complete question :

There is 1/3 gallons of water in a 3-gallon container. What fraction of the container is filled? 1. Write a multiplication equation and a division equation to represent the situation. Use "?" to represent the unknown quantity. Do not use parentheses in either of the equations.

Answer:

1 /9

Step-by-step explanation:

Capacity of container = 3 gallons

Amount of gallons in container = 1/3 gallon.

Fraction of water in container:

Division equation :

Amount of gallon in container / capacity of container

1 /3 ÷ 3 = 1/ 9

Multiplication equation :

1/3 of 1 gallon

Capacity of container = 3 gallons

1/ 3 * inverse of 3

1/3 * 1/3 = 1/9

A piston rises to 5 cm and falls to 3 cm in such a way that it returns to the maximal height three times every two seconds. If we start observing the piston at its maximal height, find an equation modelling the height, h, t seconds from the initial observation.

Answers

Answer:

(1 cm)cos3πt

Step-by-step explanation:

Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft

where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.

Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations  = 2 s

So, f = 3/2 s =1.5 /s = 1.5 Hz

Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm

h = Acos2πft

= (1 cm)cos2π(1.5Hz)t

= (1 cm)cos3πt

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