ΔABC is an equilateral triangle with AD perpendicular to BC. Prove that ΔADB ≅ ΔADC.

Answers

Answer 1

Step-by-step explanation:

An equilateral triangle means all sides are congruent.

AB≅BC≅AC

All angles are also congruent.

∠ABC≅∠BCA≅∠CAB

AD being perpendicular makes it a bisector of both BC and ∠CAB.

BD≅CD

∠BAD≅∠CAD

Now, there are multiple ways to prove that ΔADB≅ΔADC. All 3 sides and all 3 angles of both triangles are congruent, so you could do it however you want.

1) ASA (one of the possible ASA combinations)

∠ABD ≅ ∠ACD because this is an equilateral triangleBD ≅ CD because AD bisects BC∠BDA ≅ ∠CDA because AD is perpendicular to BC, both 90°

2) HL (again, one of the multiple possible HL combinations)

AD is perpendicular to BC, creating 2 right trianglesAB ≅ AC because ΔABC is equilateralAD ≅ DA by the reflexive property, it is congruent to itself

There are many more but I won't write them all out.

ABC Is An Equilateral Triangle With AD Perpendicular To BC. Prove That ADB ADC.

Related Questions

Find the 75th term of the following arithmetic sequence.
2, 8, 14, 20,
..

Answers

Answer:

The 75th term is 446

Step-by-step explanation:

Using the explict formula you get an=6n-4

you plug in 75 for n which means 75 x 6 =450 and the subtract four which gets you 446

Answer:

446 is the 75th term

Step-by-step explanation:

This sequence increases by 6

2 8 14 20 26 32 38 44 50 56 62 68 74 80 86 92 98 104 110 116 122 128 134 140 146 152 158 164 170 176 182 188 194 200 206 212 218 224 230 236 242 248 254 260 266 272 278 284 290 296 302 308 314 320 326 332 338 344 350 356 362 368 374 380 386 392 398 404 410 416 422 428 434 440 446

Which of the following is equal to this expression? (254 * 64) 1/4

Answers

Answer:

4064

Step-by-step explanation:

254*64=16256*1/4=4064

HELP

One chocolate bar and two coconut bars contain 780 calories. Two chocolate bars
and one coconut bar contains 786 calories. Find the number of calories in each kind
of bar.

Answers

Answer:

Choc Bar: 258 cals

Coco Bar: 264 cals

Step-by-step explanation:

What we can do here is something called making a system of equations.

Let us name the choc. bars x and the coco. bars y.

Then, we can get:

x+2y=780

2x+y=786

Next, we solve for x in the first equation

x=780-2y

Now, we can substitute:

2(780-2y)+y=786

1560-3y=786

-3y=-774

y=258

x=780-516

x=264

8.
Use vertex form to write the equation of the parabola.
A. y= 3(x - 2)^2 - 2
B. y= (x + 2)^2 + 2
C. y= 3(x + 2)^2 + 2
D. y= 3(x - 2)^2 + 2

Answers

Answer:

C. y= 3(x + 2)^2 + 2

Step-by-step explanation:

A. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , − 2 )

B. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

C. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

D. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , 2 )

What is the least common denominator for 5 and 16

Answers

The least common denominator for 5 and 16 is 80

Answer: 80

Step-by-step explanation:

16, 32, 48, 64, 80

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 75, 80

please help i dont understand this!

Answers

Answer:

Pmt Amt     $12.50      $23.50      $64.00      $82.00

Fee             $0.25        $0.47        $1.28         $1.64

Step-by-step explanation:

The top line is the payment amount.

The bottom line is the 2% fee.

Let's do the middle columns first.

For any payment amount, the fee is 2%.

To find a percent of a number, change the percent to a decimal by moving the decimal point of the percent to places to the left, and multiply the decimal by the number.

2% as a decimal is 0.02

To find 2% of a number, multiply 0.02 by the number.

The second column has payment amount of $23.50

We need to find 2% of $23.50

2% of $23.50 = 0.02 × $23.50 = $0.47

The third column has payment amount of $64.00

We need to find 2% of $64.00

2% of $64.00 = 0.02 × $64.00 = $1.28

Now we do the first and 4th columns. Here we know the fee, and we are looking for the payment amount.

Let the amount be x.

The fee is 2% of x, so the fee is

0.02x

We set the expression equal to the actual fee and solve for x.

The first column has a fee of $0.25

0.02x = $0.25

x = $0.25/0.02

x = $12.50

The 4th column has a fee of $1.64

0.02x = $1.64

x = $1.64/0.02

x = $82

Answer:

Pmt Amt     $12.50      $23.50      $64.00      $82.00

Fee             $0.25        $0.47        $1.28         $1.64

Math help because I forget

Answers

Answer:

R.I.P

Step-by-step explanation:

goodluck doing that

The product of −2 and a number x is greater than 30. Whats the solution of the inequality.


Answers

Answer:  x < -15

Step-by-step explanation:

(-2)*(x) > 30

x < -15  The inequality reverses direction when a negative number is used in the manipulation (we divided by -2).

test ill give brainlist
Subtract.

7/8−4/8

Answers

Step-by-step explanation:

7/8 - 4/8.....find the common denominator

(7-4)/8 .....the common denominator is 8

3/8

hope this helps

what part of 3 dollars are 25 nickels

Answers

Answer:

25 nickles are 5/12ths of a dollar

Step-by-step explanation:

25*5=125, or $1.25. Now we make this a fraction, we get 1.25/3, or 5/12

The 25 nickels are the 5/12 part of the 3 dollars.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that 1 nickel = 0.05 dollars.

Then the number of dollars in 25 nickels will be given as,

⇒ 25 x 0.05

⇒ $1.25

Divide the number 1.25 by 3. Then we have

⇒ 1.25 / 3

⇒ 5 / 12

The 25 nickels are the 5/12 part of the 3 dollars.

More about the Algebra link is given below.

https://brainly.com/question/953809

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Opps, forget to add picture. 6 minutes left. Pls help, thank you!

Answers

Answer:

I don't know sorry please forgive me

Answer:

D

Step-by-step explanation:

mean is 11.25 and midian is 10.50

HELPPPPPPPPP
A: 5 units
B: 4 units
C: 3 units
D: 2 units

Answers

Answer:

Its 5 units why its simple X and Y is in a strait line which mean you measure it and divide it by 3.14 which is pie you get your answer.

Step-by-step explanation:

mark brain if im correct :D

Find the distance between the two points in simplest radical form. Please help! <3​

Answers

Answer: on the bottom is (-6,5) and on the top is (1,7)

Step-by-step explanation:

What is the discriminant of the quadratic equation 9x^2+5x-9=0

Answers

Answer:

Δ = 349

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is

Δ = b² - 4ac

9x² + 5x - 9 = 0 ← is in standard form

with a = 9, b = 5 , c = - 9 , then

b² - 4ac

= 5² - (4 × 9 × - 9)

= 25 - (- 324)

= 25 + 324

= 349

help asap for brainlist

Answers

Answer:

l=A/W

Step-by-step explanation:

Example:

Area = 500 m^2

w= 10m

L= Area/ W

L=500/10

L=50

To check this

A= L*W

500=50*10

B: L = A/w
Explanation: if your finding length you just have to get L by itself so you would divide by w to get w on the other side which would get you A divided by w

Like terms can be ________

this is fill - up question


Answers

Answer:

.the same variables and same powers

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers.

HOPE IT HELPS...............

find the nth term in the following sequesnce: 1, 3, 9, 27​

Answers

Answer:81

Step-by-step explanation: it is skip by 3x so 21 x3 = 81

:)

Brian, Pip and Sara share some sweets in the ratio 4:2:1. Brian gets 45 more sweets than Sara. How many sweets are there altogether?

Answers

Answer:

105 sweets

Step-by-step explanation:

4×15 = 60

2×15=30

1×15=15

60-15 =45

60+30+15=105

Find the slope of the line

Answers

The slope is -1/2!
Slope is rise/run
So if you count the rise and run between two point on the graph you will know:)
It is negative because the line is heading down

I need help to divide fractions

BTW I'm in 5th grade

Answers

I can help, what is the question?

Find the slope of the line that passes through the point (-3,20), (12,15)

Answers

So the formula to use is (y2-y1)/(x2-x1) so that would be (15-20)/(12-(-3) then that become -5/15 and then the answer would be -1/3 hope this helps

Can you please help me

Answers

Answer:

11

Step-by-step explanation:

help for brainliest plz help i am stuck at thing

Answers

Answer:

= cot²A

Step-by-step explanation:

ito na po step by step explanation

[tex](1-sin^{2}A)(1+cot^{2}A) = cos^{2}A .\frac{1}{sin^{2}A } = \frac{cos^{2}A }{sin^{2}A } = (\frac{cosA}{sinA} )^{2} =cot^{2}A[/tex]

ok done. Thank to me :>

What is the equation of the line perpendicular to y = -4x + 3 that goes through (8, -3)?

Answers

Perpendicular slope: opposite and reciprocal
-4 opposite and reciprocal = 1/4
Y = 1/4x + b
Plug in point
-3 = 1/4(8) + b
-3 = 2 + b, b = -5
Solution: y = 1/4x - 5

What is the answer to n?

Answers

Answer:

n = 108

Step-by-step explanation:

The three medians of a triangle intersect at the same point inside the triangle.

The segment from a vertex to the point in the center is 2 times as long as the

other part of the median line.  So OC is 2 times KC.

KC =108    

OC = 2(108)

2n + 10 = 216

2n = 206

n = 108

In ΔABC , Value of [tex]n= 31[/tex] as per given condition of median of a triangle .

What is median of a triangle?

" Median of a triangle is defined as the line segment passing the vertex of a triangle and intersect at mid point of its opposite side.Intersecting point of three medians is known as Centroid."

Property used

Centroid divides the median in the ratio of [tex]2:1[/tex] from vertex side.

According to the question,

Given,

In ΔABC,

BL, AM, CK are the medians of a triangle ABC.

'O' represents the Centroid

[tex]KC = 108\\\\OC = 2n +10[/tex]

Ratio of [tex]KC : OC = 3: 2[/tex]

Substitute the value of KC and OC we get,

[tex]108 : (2n + 10) = 3:2\\\\\implies 3 (2n+ 10) = 2(108)\\\\\implies 6n + 30 = 216\\\\\implies 6n = 186\\\\\implies n = 31[/tex]

Hence, in ΔABC , Value of [tex]n= 31[/tex] as per given condition of median of a triangle .

Learn more about median of a triangle here

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Which expression simplifies to 5√3?

Answers

Answer:

C.

[tex] \sqrt{75} [/tex]

Step-by-step explanation:

You can just enter it in the calculator to see which is equal to

[tex]5 \sqrt{3} [/tex]

A gym is offering a deal to members. Customers can sign up by paying a registration fee of $100 and $28 per month. The function that models this situation is c(m) = 28m + 100, where m is the number of months and c(m) is the cost of becoming a member.
Determine:
6. the shape of the graph



7. the independent and dependent variables


8. the domain and range


9. Interpret the slope and y-intercept values


10. How much will the membership cost for a whole year?

Answers

6) The equation given is written in standard form of writing the equation of a line y = mx + b

Hence the shape of the graph that denotes the equation c(m) = 28m + 100 is a straight line

7) The independent variable is a variable that can stand alone while the dependent variable is depending on all other variables in an expression.

From the given equation c(m) = 28m + 100, the independent variable is (m) while the dependent variable is c(m)

8) The domain is the input value for which the equation exists while the rage is the output value for which the equation exists. For the given expression, the value of the expression will exist at a point where c(m) > 0

28m + 100 > 0

28m > -100

m > -100/28

m > --25/7

The domain is m > -25/7 while the range is c(m) > 0

9) The comparing the equation with y = xm+ b

where x is the slope

28m = mx

x = 28

This shows that the rate of change of cost per member is $28

The y-intercept is the point where the number of months is 0

If m = 0

c(0) = 28(0) + 100

c(0) = 100

The initial cost of membership in the first month is $100

10) Given the formula c(m) = 28m + 100

For a whole year, m = 12

c(12) = 28(12) + 100

c(12) = 336 + 100

c(12) = 436

Hence the membership will cost $436 for the whole year

Learn more here:  https://brainly.com/question/17003809

5p + 3 = 15

Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.

Answers

Well a2bsi and that is perfect emails of the snake that the parthagreom Theron form the itian monarch

The given expression represents a number whose 5 times is 3 less than 15 which is 12/5.

Given that,
An expression is given we have to discuss what the expression 5p + 3 = 15 implies.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
5p + 3 = 15
5p = 15 - 3
p = 12 / 5

Thus, the given expression represents a number whose 5 times is 3 less than 15 which is 12/5.

Learn more about simplification here:

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х
4.
1
6 11
y
-3
-2
-1
0
slope:

Answers

Answer:

slope = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (11, 0) ← 2 ordered pairs from the table

m = [tex]\frac{0-(-3)}{11-(-4)}[/tex] = [tex]\frac{0+3}{11+4}[/tex] = [tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]

three are 6 blades on each windmill. how many total blades are on 7 windmills? use a fives fact to solve

Answers

Answer: 42 I think

Step-by-step explanation:

I did 6 times 7

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