Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
Answers
The theorem that would be included in the proof is: CPCTC theorem.
What is the CPCTC Theorem?CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.
To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:
1. angle D ≅ angle F [given]
2. angle DBE ≅ angle ECF [given]
3. side DE ≅ side EF [given]
4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]
5. DB ≅ FC [by the CPCTC theorem]
With the given proof, we can state that side DB is congruent to side FC.
Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.
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Related Questions
The greatest common factor(GCF) of LaTeX: x^7,\:x^3,\:x^5\:is\:_{ }__________.
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Answer:
x^3Step-by-step explanation:
We are to find the greatest common factor of x^7, x^3 and x^5
x^7 = x^3 * x^4
x^3 = x^3 * 1
x^5 = x^3 * x^2
From both factors, we cam see that x^3 is common to the three, hence the GCF is x^3
When a point is reflected across a line of reflection, it remains the same distance from the line.True or False
Answers
Answer:
True
Step-by-step explanation:
To answer this question, I will use the following illustrations.
Assume a point (x,y) is reflected across the x-axis.
Using reflection rule, the new point will be: (x,-y)
On a coordinate plane, the x-axis is represented as: (x,0)
So, we will calculate the distance between (x,y) and (x,0) and also calculate the distance between (x,-y) and (x,0) using the following distance formula.
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Distance between (x,y) and (x,0)
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]D= \sqrt{(x - x)^2 + (0 - y)^2}[/tex]
[tex]D= \sqrt{(0)^2 + (- y)^2}[/tex]
[tex]D= \sqrt{0 + y^2}[/tex]
[tex]D= \sqrt{y^2}[/tex]
[tex]D = y[/tex]
Distance between (x,-y) and (x,0)
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]D= \sqrt{(x - x)^2 + (0 - (-y))^2}[/tex]
[tex]D= \sqrt{(0)^2 + (0+y)^2}[/tex]
[tex]D= \sqrt{0 + y^2}[/tex]
[tex]D= \sqrt{y^2}[/tex]
[tex]D = y[/tex]
See that the calculated distance are equal.
Hence, the given statement is true
Which equation represents how much it would cost for any number of rides? * 1 point r = 1.50c c = r - 1.50 r = 1.50 + c c = 1.50r
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Kim got to the store at 11:19 in the morning. She spent 24 minuets in the store how many minuets after she got to the store and left?
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Answer:
11:43 am
Step-by-step explanation:
Given data
Time of arrival= 11:19 am
We are told that she spent 24 minutes in the store
Based on this, we can estimate the time she left the store
The time she left
=11:19+ 24
=11:43 am
Hence she left 11:43 am
Use algebra tiles to find the difference. Let one yellow tile equal +1 and one red tile equal –1. 12 – (–9)
Answers
Answer:
21
Step-by-step explanation:
12 - (-9)
Open The bracket :
Recall: - * - = +
Hence,
12 + 9 = 21
Calculate the unit price of the following item:
Chocolate chip cookies cost $2.79 per package and
there are 30 cookies inside. What is the price per
cookie? *
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 this is the one i need help with please !! honors algebra 2 , 10th grade
Answers
Answer:
g(g(x)=25x
Step-by-step explanation:
g(g(x) is a composition function. Think of g(x) as input. That means whatever g(x) equal that will be inside of the function g(x)
g(x) equal 5x so 5x will be the equal value going into the function g(x)
[tex]g(x) = 5x[/tex]
[tex]g(x) = 5(5x)[/tex]
Which equal 25x
what's the answer for 1/2 of 3/5?
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Answer:
3/10
Step-by-step explanation:
what is the equivalent Ratios to 18:15
Answers
Answer:
6:5 in simplest form
Step-by-step explanation:
Answer:
6:5
Step-by-step explanation:
The greatest common factor, and only shared factor is 3. Use three and divide on both sides to get 6 and 5
The standard form of y = 5(x + 4)(x + 5) is
Answers
Answer:
mark me as brainliest plz
Answer:
21 is Correct answer hope you will like it
Nathan Reynolds bought a car for $15,000. He made a down payment of $3,000. Nathan secured a loan for the balance of the purchase price at 8 percent interest for four years.
determine the monthly payment and total interest
Answers
Answer:
1) The monthly payment is approximately $292.96
2) The total interest is approximately $2,061.84
Step-by-step explanation:
1) The financing method Nathan Reynolds applied to buy the car is given as follows;
The purchase price of the car = $15,000
The down payment made for the car = $3,000
The
The interest on the loan he took for the balance of the purchase price, R = 8%
The number of years for which he took the loan, n = 4 years = 48 months
We have;
The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)
∴ The balance of the purchase price = $15,000 - $3,000 = $12,000
The balance of the purchase price = $12,000 = The loan Nathan secured
The monthly payment on a loan is given by the following formula
[tex]A = P \times \dfrac{r \cdot (1 + r)^n}{(1 + r)^n - 1}[/tex]
Where;
A = The payment amount made monthly
P = The principal or loan amount = $12,000
r = The interest rate divided by 12 = R/12 = 8/12 = 2/3
n = The number of months the monthly payment will be made = 48 months
By plugging in the variable values, we get;
[tex]A = 12,000 \times \dfrac{\dfrac{2}{300} \times \left (1 + \dfrac{2}{300} \right ) ^{48}}{ \left (1 + \dfrac{2}{300} \right )^{48} - 1} = 292.955068099 \approx 292.96[/tex]
Therefore, the payment amount made monthly, A ≈ $292.96
2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84
The total payment made in the 48 months ≈ $14,061.84
The total interest = (The total payment made in the 48 months) - (The loan amount)
∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84
Find g. 45° 45°
[tex] 3\sqrt{2} [/tex]
Write your answer in simplest radical form, units
Answers
Answer:
sin45=3√2/g
g=3√2/(1÷√2)=3×√2×√2=3×2=6units
Answer: 6 (the math sign that’s like a checkmark i thinks it’s square root) 2. So like 6/2 you get the point.
Step-by-step explanation: I just had this problem on ixl and it gave me the answer
the graph of y=-3x+2, state the domain and the range
Answers
Answer:
Domain: (-∞,∞)
Range: (-∞, ∞)
Hope this helps.
39°
.(91-x9)
What solves for x
Answers
Since Beth was born, the population of her town has increased at a rate of 850 people per year. On Beth's 9th birthday, the total population was nearly 307,650, Write and solve a linear equation to find the population on Beth's 16th birthday.
I only need the equation pls help
Edit: the equation needs to be in slope intercept form
Answers
Answer:
editor edit
37,650
Step-by-step explanation:
37650
Answer the photo below thanks
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Answer:
I think its D
Step-by-step explanation:
7.1 as a percentage
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Answer:
its 710%
Step-by-step explanation:
710% hope it helps!
I NEED HELP PLEASE. I WILL GIVE BRAINLIST IF RIGHT!
Answers
Answer:
Shift f up by 1 unit
Step-by-step explanation:
The email address lol
50 points for this helpppp plzz
Answers
Answer:
ok
Step-by-step explanation:
Answer:
srry I needed the points hope u don\t mind
Step-by-step explanation:
find the side of the square whose perimeter 20 m
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If 91 is 1% of a number, what is that number? *
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Answer:
The Answer is 1900.
Answer:
9100
Step-by-step explanation:
multiply the one percent by 100 to get the 100 percent
find the missing measure
Answers
Answer:
Step-by-step explanation:
A typical person takes about 24000 breaths each day. Write an equation you can use to find the number of breaths a typical person takes each minute.
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Step-by-step explanation:
Welp if a typical person takes 24000 breaths each day that's means
24000÷24=1000
so that's means 1000 per hour
if a hour take 60 Min that's mean
1000÷60=16.6666667 don't tell me I'm not sure about this answer and not really good at this :p
can someone please help me??
Answers
Answer:
There is only one solution and it is the point of intersection
Step-by-step explanation:
A = 5x^2+3xy-7y^2 B = -x^2+2xy+8y^2 B, minus, A, equals
I WILL GIVE BRAINLYIST!!!!!!!!!!! Help!!!!!
Answers
Answer: -6x^2-xy+15y^2
Step-by-step explanation:
The value of B-A is -6x²-xy+15y² .
What is an Equation ?A statement where the algebraic expressions are equated with an equal sign with each other is called an Equation.
It is given that
A = 5x²+3xy-7y²
B = -x²+2xy+8y²
To calculate is B - A
B- A = ² (-x²+2xy+8y²) - (5x²+3xy-7y² )
B-A = -x²+2xy+8y² - 5x²- 3xy +7y²
B-A = -6x²-xy+15y²
Therefore the value of B-A is -6x²-xy+15y² .
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one hundred twenty-three and thirty hundreths. in decimal form
Answers
Answer:
0.2330
Step-by-step explanation:
A cake recipe calls for 2 1/4 cups of flour. Mrs Allen measured 3/4 cup of whole wheat flour and plans to use bleached flour for the remainder. How much bleached flour should she use?
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Answer:
she should use 1 2/4 cups of bleached flour
help me please i have no idea what i’m doing
Answers
Answer:
1. 5
2. 5/3
3. 4.5
4. 21
5. 10
6. (-12
7. (-1.5
An arithmetic sequence has second term 28 and the fifth term 52. (3 marks) a. Find u1 and d. b. Find u10
Answers
Answer: See explanation
Step-by-step explanation:
Second term = a + d = 28 ....... i
Fifth term = a + 4d = 52 ......... ii
Subtract equation I from ii
3d = 24
d = 24/3 = 8
d = common difference = 8
Since a + d = 28
a + 8 = 28
a = 28 - 8 = 20
First term = a = 20
u10 = a + (n-1)d
= a + (10-1)8
= 20 + (9 × 8)
= 20 + 72
= 92
Eric and Kelsey each work after school to earn money. Eric charges $10, plus an additional $4 per hour to babysit. Kelsey charges $15, plus an additional $3 per hour to rake. Eric and Kelsey work the same number of hours. Which system of equations can be used to determine how many hours, x, they need to work to earn the same amount of money, y?
Answers
Answer:
the option 3 or c is correct