Given that △ABC is an isosceles triangle with AB⎯⎯⎯⎯⎯≅AC⎯⎯⎯⎯⎯ and AD⎯⎯⎯⎯⎯ bisecting ∠BAC, which of the following proves that ∠ABD≅∠ACD?

Answers

Answer 1

The isosceles triangle having an angle bisector [tex]\overline{AD}[/tex] forms two congruent triangles.

ΔBAD ≅ ΔCAD, therefore, ∠ABD ≅ ΔBAD, by CPCTC

Reasons:

The given parameters are;

ΔABC is an isosceles triangle.

[tex]\overline{AB}[/tex] ≅ [tex]\overline{AC}[/tex]

[tex]\overline{AD}[/tex] bisects ∠BAC

Therefore, the proof that ∠ABD  ≅ ∠ACD is given as follows;

1. [tex]\overline{AB}[/tex] ≅ [tex]\mathbf{\overline{AC}}[/tex] (Given)

2. [tex]\overline{AD}[/tex] bisects ∠BAC (Given)

3. ∠BAD ≅ ∠CAD (Definition of angle bisector)

4. [tex]\overline{AD}[/tex] ≅ [tex]\mathbf{\overline{AD}}[/tex] (Reflexive property of congruency)

5. ΔBAD ≅ ΔCAD (Side Angle Side, SAS rule of congruency based on steps 1, 3 and 4)

6. ∠ABD ≅ ∠ACD (Congruent Parts of Congruent Triangle are Congruent, CPCTC)

Learn more about SAS rule of congruency here:

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Given That ABC Is An Isosceles Triangle With ABAC And AD Bisecting BAC, Which Of The Following Proves

Related Questions

X=?

38 degrees 75 degrees

Answers

sum of angle of triangle is 180°

A+B+C = 180

38°+75°+ X = 180°

113° + X = 180°

X = 180° -113

X = 67°

Answer:

67

Step-by-step explanation:

Help find initial value for graph PLSSSSSS the dotted points are (0,8) and (16,20)

Answers

Answer:8

Step-by-step explanation:

The initial value, or y-intercept, is the output value when the input of a linear function is zero, as you've already pointed out, the function crosses the y- axis at (0,8)

Convert 45 mi/hr to feet per minute

Answers

Answer:

3960

Step-by-step explanation:

multiply 45 by the amount of feet in a mile (5280)

take that answer and divide in by how many minutes are in an hour

answer the question about the following polynomial

Answers

theres nothing there, i can’t help you sorry

Find the slope of the line passing through the points (-6, 1) and (-7,5).

Answers

Answer:

y = -4x – 23

Hope this helps :)

Slope= y2-y1/x2-x1

= 5-1/-7-(-6)

= 4/-1

= -4

Check whether (19/9, 15/3) is
a solution of the equation 3a + b = 8 or
not where (a,b) is co-ordinate point.​

Answers

Answer:

No, it is not a solution to the equation.

Step-by-step explanation:

If [tex]( \frac{19}{9} , \frac{15}{3} )[/tex] is a solution of the equation, the left-hand side (LHS) of the equation would equal to the right-hand side (RHS) of the equation.

3a +b= 8

When a= [tex] \frac{19}{9} [/tex], b= [tex] \frac{15}{3} [/tex],

LHS

= [tex]3( \frac{19}{9} ) + \frac{15}{3} [/tex]

[tex] = \frac{19}{3} + \frac{15}{3} [/tex]

[tex] = \frac{34}{3} [/tex]

[tex] \frac{34}{3} ≠8[/tex]

Since the left-hand side is not equal to the right-hand side of the equation, [tex]( \frac{19}{9} , \frac{15}{3} )[/tex] is not a solution of the equation.

Given equation is 3a+b = 8

Given point = (19/9,15/3)

Put a = 19/9 and b = 15/3 in LHS of the given equation then

⇛ 3(19/9)+(15/3)

⇛(19/3)+(15/3)

⇛ (19+15)/3

⇛ 34/3 ≠ 0

LHS ≠ RHS

Given point not satisfies the given equation

Therefore, it is not the solution of the given point.

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What is the value of a in the equation 3a + b = 54, when b = 9? 15 18 21 27..

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- 3m + 7 - 2n


Can I get the answer

Answers

Answer:

3m + 5

Step-by-step explanation:

uhmm i think 2n is i cant solve here hope it helps

A website is selling couches for $864. The site got the couches at a cost of $320. What percentage is the mark-up?

Answers

That is a 170% markup

Juliet needs to rewrite 3 (x 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get 3 (2 x) = 6 y. She could divide both sides by 3 to get x 2 = 2 y. She could distribute the 3 to get 3 x 2 = 6 y. She could subtract the 6y to get Negative 6 y = 3 (x 2).

Answers

The step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y

Note that the standard equation of a line in slope-intercept form is expressed as y = mx + b

m is the slopeb is the y-intercept

Given the function 3(x+2)=6y, for Juliet to write in slope-intercept form, the best approach is to first divide both equations by 6 as shown:

[tex]3(x+2)=6y \\\frac{3(x+2)}{6} =\frac{6y}{6} \\\frac{x+2}{6}=y[/tex]

Swap sides

[tex]y=\frac{x+2}{6}\\y=\frac{1}{6}x +\frac{1}{3}[/tex]

She could as well distribute the 3 over x + 2 to have:

3(x + 2) = 6y

3x + 3(2) = 6y

3x + 6 = 6y

Hence based on the option, the step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y

Learn more on distributive law here: https://brainly.com/question/25224410

Answer:

Its C

Nevermind Its Not its A or B

Step-by-step explanation:

:)

Work out the difference between 38.3 and 1.72​

Answers

Answer:

36.58

Step-by-step explanation:

38.3-1.72=36.58

The value of the expression 38.3 - 1.72 will be 36.58.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

38.3 and 1.72​

Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 38.3 - 1.72

⇒ 36.58

The value of the expression 38.3 - 1.72 will be 36.58.

More about the Algebra link is given below.

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Does (–2, –2) make the equation y = x true?

Answers

Answer:

Yes.

Step-by-step explanation:

According to the given co-ordinate.

(x,y) = (-2,-2)

i.e. x = -2, y = -2

So, We can say that x = y = -2.

Hence, the given co-ordinate makes the equation y = x true.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

1. What is the exact distance from (-4,-2) to (4, 6)?
O 24 units
O 188 units
O V100 units
O V128 units

Answers

V100 Units I hope that's help

The table shows the distance between Greenville and nearby towns. The distance between Astaville and
Greenville is 14 miles less than the distance between Greenville and Jonesborough,
Distance between Greenville and
Nearby Towns(miles)
Jonesborough
24
Willfower 21
Maybem 30
Part 1 out of 2
Enter two equations that state the relationship of the distances between the three towns. Use x as the
variable

Answers

That looks so hard dude i feel bad-
Hdjdajahsidndisbaiwbtd

The diameter of Mercury is approximately4.9×103 kilometers. The diameter of Saturn is approximately 1.2×105 kilometers. About how many times greater is the diameter of Saturn than the diameter of Mercury?

Answers

Answer: 378.7 kilometers (maybe, I am not sure)

Mercury: 4.9 * 103 = 504.7 kilometers

Saturn: 1.2 * 105 = 126 kilometers.

Why on earth is Mercury's diameter greater than Saturn's -

504.7 - 126 = 378.7 kilometers

What is the range of possible sizes for side x?

Answers

Answer:

x = 3.96

Step-by-step explanation:

apply the pitagoras theorem

x =

[tex] \sqrt{ {2.8}^{2} + {2.8 }^{2} } [/tex]

If the two legs of one right triangle are congruent to the two legs of another right triangle, then the two triangles are congruent.
a) True
b) False

Answers

Answer:

Step-by-step explanation:

This only happens with right triangles. You need only 2 legs. The reason is that the two legs given are the arms of the right angle so secretly you are using SAS. The right angle is enclosed by the two legs, and that must be stated among your givens.

So the answer to the question is true.

Please help me Find the slope please no links or bots please and thank you please actually help me please

Answers

Answer:

-1/2

Step-by-step explanation:

The first point is (-3,0) and the second point is (-1,-1). To find slope you do change in y over change in x. So (-1-0)/(-1--3) or -1/2 which is your slope.


Algebra 1
Q.13 Complete a function table from an equation 273
Complete the table.
f(x) = 2x - 10
х f(x)
6
7
8
9
Submit

Answers

Answer with step-by-step explanation:

To solve this, all we have to do is replace x in 2x - 10 with the number from the table.

6: 2(6) - 10 = 2

7: 2(7) - 10 = 4

8: 2(8) - 10 = 6

9: 2(9) - 10 = 8

There you have it! Have a good day :)

27.if 2 lbs of rice is $3. How much will 15 lbs of rice be?​

Answers

Answer:

2 lbs rice= $3

15 lbs rice= x

x= 15×3/2

=45/2=22.5

For $22.5 will be 15 lbs of rice .

solve 3x/7= 1/2

pls show working out thanks <3

Answers

Multiply the equation by 7, than divide by 3 to get x = 1.1666

Joan purchased a refrigerator for $1,200. She made a down payment of $65 and paid
$121 a month for 11 months. Find the total installment price of the refrigerator.

Answers

Pretty sure you set up a proportion somehow, keep months and $ separate… for example, $ over months, then $ over x… not for sure…

The total installment price is $1331.

What is an installment?

Installment means adding the total principal of the loan and the total interest on the principal together and then dividing the sum by the number of installment payments.

For the given situation,

The purchase price of the refrigerator = $1200

Down payment = $65

Monthly installment = $121

Installment period = 11 months

Total installment price = [tex](121)(11)[/tex]

⇒ [tex]\$1331[/tex]

Hence we can conclude that the total installment price is $1331.

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If RV = x+6, US = 5x-9, and RS = 11, find VT and ST

Answers

The values of VT and ST for the given rectangle are 13 and 23.56 respectively.

The given parameters:

RV = x + 6US = 5x - 9RS = 11

The value of VT and ST is calculated as follows;

from the given diagram we can conclude the following;

2RV = RT = US

[tex]2(x + 6) = 5x - 9\\\\2x + 12 = 5x - 9\\\\12 + 9 = 5x - 2x\\\\21=3x\\\\x = 7[/tex]

RT = 2RV = 2VT = 2(7 + 6) = 26

VT = ¹/₂ x 26

VT = 13

The value of ST can be determined from Pythagoras theorem as follows;

[tex]ST = \sqrt{RT^2 - RS^2} \\\\ST = \sqrt{26^2 - 11^2} \\\\ST = 23.56[/tex]

Learn more about Pythagoras theorem here:  https://brainly.com/question/12306722

asdfasdfasdfasdfasdfasdfasdfasdfasdfasdfasdf

Answers

Answer:

Asdfasdfasdfasdfasdfasdfasdfasdfasdfasdfasdf

Step-by-step explanation:

Asdfasdfasdfasdfasdfasdfasdfasdfasdfasdfasdf

What is three minus X equals 11

Answers

Answer:

x= -8

Step-by-step explanation:

Subtract 3 from both sides to isolate the variable

Divide the variable by -1 so it can become positive; whatever you do to one side, you have to do to the other.

You'll end up with the equation of x= -8 if you do it correctly

-x=11-3 x=8 this is anwer

l= prt is an example of.

Answers

Answer:

intrest=principle*rate* time

Step-by-step explanation:

Base formula, written as I = Prt or I = P × r × t where rate r and time t should be in the same time units such as months or years. Time conversions that are based on day count of 365 days/year have 30.4167 days/month and 91.2501 days/quarter.

the side length of a square is n cm.

Answers

Answer:

  (c)  Alicia, Bart, and Diego's answers are equivalent

Step-by-step explanation:

The perimeter of a square is the sum of the side lengths

  n + n + n + n . . . . . Alicia's answer

  = (n +n) +(n +n) = 2n +2n . . . . . Diego's answer

  = (2 +2)n = 4n . . . . . . Bart's answer

Alicia, Bart, and Diego's answers are equivalent.

if a/b-d=2c/b, find the value of c when a=3 b=4 and d=5
please explain your answer

Answers

Answer:

c= -17/2

Step-by-step explanation:

a/b-d=2c/b

3/4-5=2c/4

-17/4=2c/4

-17/4÷1/4=2c

-17/4×4=2c

2c=-17

c=-17/2

How many centimeters equal 128.9 meters?.

*Enter you answer in the box*

|___| cm

Answers

12890 centimeters

Hope this helped :)

Given that two terms of an arithmetic sequence are u5 = -3.7 and u15 = -52.3, find the value of the 19th term. ​

Answers

Answer:

  a19 = -71.74

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

The given 5th and 15th terms tell us ...

  -3.7 = a1 +d(5 -1)

  -52.3 = a1 +d(15 -1)

Subtracting the first of these equations from the second, we find ...

  10d = -48.6

  d = -4.86 . . . . . . divide by 10

The 19th term will be ...

  a19 = a1 +d(19 -1)

Subtracting the 15th term from this, we find ...

  a19 -a15 = 4d

  a19 = 4d +a15 = 4(-4.86) +(-52.3)

  a19 = -71.74

Which rule was used to create the input/output?

Answers

The answer should be A i think

Answer:

B. y = -4x

Step-by-step explanation:

input x in the possible answers

y = -4x

-4(2) = 8

-4(1) = -4

-4(-3) = 12

-4(-5) = 20

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