Match the reasons to the statements given.
Given:
ABCD
EF contains T
Prove:
ET = FT
Answers
Answer:
The reasons and the statements are given as follows;
1. Parallelogram ABCD [tex]{}[/tex] Given
2. BT = TD [tex]{}[/tex] Diagonals of parallelogram bisect each other
3. ∠1 = ∠2 [tex]{}[/tex] Vertically opposite angles
4. BC ║ AD [tex]{}[/tex] Definition of parallelogram
5. ∠3 = ∠4 [tex]{}[/tex] If lines are parallel then alternate interior
angles are equal
6. Triangle BET congruent to Triangle DFT by ASA
7. ET = T_F [tex]{}[/tex] CPCTE
Step-by-step explanation:
Statement [tex]{}[/tex] Reason
1. Parallelogram ABCD The given quadrilateral
2. BT = TD Based on the properties of a parallelogram, the parallelogram diagonals bisect each other
3. ∠1 = ∠2 Vertically opposite angles formed by two intersecting lines are equal
4. BC ║ AD By definition, the opposite sides of a parallelogram are parallel
5. ∠3 = ∠4 Based on the property of equality of the alternate interior angles of two parallel lines
6. Triangle BET congruent to Triangle DFT by Angle-Side-Angle rule of congruency
7. ET = T_F by Congruent Parts of Congruent Triangles are Equal, CPCTE, postulate.
The reasons that matches the statements in the two-column proof is shown in the table attached in the image below.
Recall:
Based on the, CPCTE Theorem, if two triangles are congruent, all its corresponding sides and angles of both triangles are therefore congruent together.The ASA Congruent Theorem justifies that two triangles are congruent if they have two pairs of congruent angles and a pair of included sides that are also congruent.Given parallelogram ABCD, and also, we know that EF contains T, to prove that ET = FT, establish that:
ΔBET ≅ ΔDFT by the ASA Congruence Theorem, then demonstrate that ET = FT by the CPCTE Theorem.
Therefore, the reasons that matches the statements in the two-column proof is shown in the table attached in the image below.
Learn more about ASA Congruence Theorem on:
https://brainly.com/question/3168048
Related Questions
What is the value of X
D=X°
F=103°
A. 51.5°
B. 128.5°
C. 77°
D. 38.5°
Answers
if c = 42 -d is true, then which is greater: cord, or are you not able to tell? Explain how you
know your choice is correct.
Answers
Answer:
what does d equal?
Step-by-step explanation:
There are currently 73 million cars in a certain country, decreasing by 1.7% annually.
How many years will it take for this country to have 54 million cars? Round to the
nearest year.
Answers
Answer:
17.6 years
Step-by-step explanation:
There are currently 73 million cars in a certain country, decreasing by 1.7% annually.
How many years will it take for this country to have 54 million cars? Round to the
nearest year.
We use the formula
y = a(1 - r)^t
a = Initial amount = 73 million cars
y = Future amount = 54 million cars
r = decreasing rate = 1.7 % = 0.017
t = time is unknown
54,000,000 = 73,000,000(1 - 0.017)^t
Divide both sides by 73,000,000
54,000,000/73,000,000 = (0.983)^t
0.7397260274 = (0.983)^t
Take the logarithm of both sides
log 0.7397260274 = Log (0.983)^t
log 0.7397260274 =t log (0.983)
t = log 0.7397260274/log 0.983
t = -0.13092910029/-0.00744648216
t = 17.5826783005 years
Approximately = t = 17.6 years
PLEASE PLEASE PLEASE HELP!! 2 QUESTIONS WITH FUNCTIONS PLEASE!! URGENT!
Answers
Answer:
(-2, 1)16x^2 - 16x + 4Step-by-step explanation:
1.
Domain is the set of x-values
As per graph the domain is
x = (-2, 1)2.
f(x) = 4xg(x) = (x - 2)^2g(f(x)) is, replacing x with f(x) = 4x
g(f(x)) = (4x - 2)^2 ⇒ g(f(x))= 16x^2 - 16x + 4Which equation has a center at (2, 1) and a point on the circle of (2, -3)?
O (x + 2)2 + (y + 1)2 = 16
O x - 2)2 + (y - 1)2 = 4
O(x - 2)2 + (y - 1)2 = 16
O (x + 2)2 + (y + 1)2 = 4
Answers
Answer:
Option 3: [tex](x-2)^2+(y-1)^2 = 16[/tex] is the correct answer
Step-by-step explanation:
We will find the equation of the circle with given information and then compare with the choices given.
Given
Center = (h,k) = (2,1)
And point on circle = (2,-3)
The equation of circle is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
The distance between center and point on circle is the radius. So using the distance formula:
[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r = \sqrt{(2-2)^2+(-3-1)^2}\\r = \sqrt{(0)^2+(-4)^2}\\r = \sqrt{0+16}\\r = \sqrt{16}\\or\\r = 4[/tex]
Putting the values in equation of circle
[tex](x-2)^2+(y-1)^2 = 4^2\\(x-2)^2+(y-1)^2 = 16[/tex]
Hence,
Option 3: [tex](x-2)^2+(y-1)^2 = 16[/tex] is the correct answer
Answer:
c on edge
i got it right
A line with a slope of 1/2 passes through (-5,-2). Write the equation of the line in standard form.
Answers
How much interest is earned on a principal of $900 invested at an interest
rate of 13% for eight years?
Answers
Answer:
11700
Step-by-step explanation:
4j + 4j − 6j − j = 12
Solve for J
Answers
Answer:
j =12 you have to combine like terms which is all and then it will give u 12
-1.64 as a mixed number
Answers
:)
536+248 anweser please
Answers
Answer:
784
Step-by-step explanation:
Connor is working two summer jobs, making $8 per hour walking dogs and making $12 per hour landscaping.
Answers
Why is 210 divided by 30 the same as 21 tens divided by 3 tens
Answers
21 tens is equal to 210, and 3 tens is equal to 30.
Reason behind both the situations are the same are the place values of the digits.
What are the place values?According to their position in a number, each digit has a different value in mathematics, which is called place value. From the unit's starting location, these positions begin.
Ones/units, tens, hundreds, thousands, ten thousands, and so on are all ways to describe the place value of a number's digits in sequence from right to left.
Each digit in a number has a place value, which is its worth. Each digit in a number has a unique value depending on where it sits in the number. The value of a digit depends on where it falls in the number; two comparable digits in the same number may have different values.
When 210 is written in the form of place value, this will be written as 21 tens and 30 will be written as 3 tens.
Therefore, the given statement has the same values and is correct.
Learn more about place values from here:
https://brainly.com/question/1677741
#SPJ2
What is the square root of 167 -8i -4i 4i 8i
Answers
Answer:
12.922848
Step-by-step explanation:
I used my calculator
Suppose that a loan of $8000 is given at an interest rate of 16% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding ?
Answers
Answer:
9280
Step-by-step explanation:
8000 x .16 + 8000
Solve for u.
-3u = -12.99
u =
Please Hurry
Answers
Answer: u = 4.33
Step-by-step explanation:
-3u = -12.99
-3u / -3 = -12.99 / -3
u = 4.33
Kite LMNO is shown below.
What is the measure of angle M
Answers
Answer:
the answer is 78
Step-by-step explanation:
It is the largest one that i can see. The other options are cut off. If you could repost again....
Bri goes to the movies and buys three items that together sum to $11.50. Two of the items she
bought cost $3 each. Write an equation to express how much money Bri spent at the movies.
Answers
Answer:
the answer is $5.5
Step-by-step explanation:
A baseball team won 20 games and lost 10 games. What percent of the games did the team win?
33One-third%
50%
66Two-thirds%
200%
Answers
Answer:
50%
Step-by-step explanation:
10/20 is equal to 1/2, 1/2 can be rewritten as .50 or 50%
Answer check helpppp
Answers
Answer:
correct good job!!!
Step-by-step explanation:
Plz help Solve three and one half times one and two thirds
A) three and two sixths
B) four and two sixths
C) five and five sixths
D) six and five sixths
Answers
Answer:
B
Step-by-step explanation:
i will give brainliest if correct
Answers
Answer:
The surface area of the net shown is: 88 [tex]in^2[/tex]
Step-by-step explanation:
Break up the different shapes in the net:
Let's take the big square first:
It has a side of 5in and a base of 4in.
We multiply both these values to get 20[tex]in^2[/tex]
Lets look at the small rectangular box now:
It has a side of 3in and a base of 4in.
We multiply both these values to get 12[tex]in^2[/tex]
There are two big squares so we add up their surface areas:
20[tex]in^2[/tex] + 20[tex]in^2[/tex] = 40[tex]in^2[/tex]
There are 4 small rectangular squares so we add up their surface areas:
12[tex]in^2[/tex] + 12[tex]in^2[/tex] + 12[tex]in^2[/tex] + 12[tex]in^2[/tex] = 48[tex]in^2[/tex]
Now we add up the big square and small rectangular squares values:
40[tex]in^2[/tex] + 48[tex]in^2[/tex] = 88[tex]in^2[/tex]
Therefore the answer is 88[tex]in^2[/tex]
Which number is a reasonable estimate for 826x64?
А
64,000
B
50.000
6,400
D
5,000
Answers
Please help me figure out the answer to this question and the processes well!
Answers
For -3 the answer is -11 because 3(-3)-2 = -11
For 1 the answer is 1 because 3(1)-2 = 1
For 5 the answer is 13 because 3(5)-2 = 13
So your points will be (-3,-11), (1,1), and (5,13)
Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape of a right rectangular
prism and the dimensions, in inches, are 367 x 19 x 24. During the set-up, Alex fills the aquarium with 6,039
ins of water.
What percent of the volume of the aquarium is filled with water? Round your answer to the nearest whole percent.
Enter your answer in the space provided.
Answers
Answer:
4%
Step-by-step explanation:
Formula for volume of a right rectangular prism is;
V = lwh
Where;
l is length
w is width
h is height
We are given l = 367; w = 24; h = 19
Thus;
Volume is;
V_full = 367 × 24 × 19
V_full = 167352 in³
We are told that Alex filled the aquarium with 6039 in³ of water.
Thus, percentage of the aquarium filled with water is;
(6039/167352) × 100% = 3.61%
Approximating to nearest percent gives; 4%
What is the answer for 4(2p-8)-6p=20+4(p+6)
Answers
Hello! :)
[tex]\large\boxed{p = -38}[/tex]
4(2p - 8) - 6p = 20 + 4(p + 6)
Distribute the coefficients outside of the parenthesis:
4(2p) + 4(-8) - 6p = 20 + 4(p) + 4(6)
8p - 32 - 6p = 20 + 4p + 24
Combine like terms:
2p - 32 = 44 + 4p
Subtract 2p from both sides:
-32 = 44 + 2p
Subtract 44 from both sides:
-76 = 2p
Divide both sides by 2:
p = -38.
Answer p = -4
6p + 2(4 + -2p) = 3(p + 4)
6p + (4 * 2 + -2p * 2) = 3(p + 4)
6p + (8 + -4p) = 3(p + 4)
8 + 6p + -4p = 3(p + 4)
8 + 2p = 3(p + 4)
8 + 2p = 3(4 + p)
8 + 2p = (4 * 3 + p * 3)
8 + 2p = (12 + 3p)
8 + 2p = 12 + 3p
8 + 2p + -3p = 12 + 3p + -3p
8 + -1p = 12 + 3p + -3p
8 + -1p = 12 + 0
8 + -1p = 12
8 + -8 + -1p = 12
0 + -1p = 12 + -8
-1p = 12 + -8
-1p = 4
p = -4
I need help on this pls help me
Answers
Answer:
irrational numbers is in the red rectangle, rational numbers is outside both circles on the left, integers is in the purple circle, whole numbers is in the blue circle
false
true
true
true
Step-by-step explanation:
Whats The RiGhT answer giving brainliest
Answers
Answer:
D is correct because its the only graph that displays the first set of data correctly.
What is the multiples of 46
Answers
Answer:
0, 46, 92, 138, 184, 230, 276, 322, 368, 414, 460, 506, 552
Step-by-step explanation:
multiples up until 12
Answer:
46,92,138,184,230,276,322,368,414,460
Step-by-step explanation:
Write the difference of two algebraic expressions modeled by the algebra tiles. Let $x$ be the variable. Then use the algebra tiles to simplify the expression. Two groups of algebra tiles. The second is subtracted from the first. The first group has two positive variables tiles and seven positive unit tiles. The second group has two positive variable tiles and four negative unit tiles.
Answers
Answer:
3
Step-by-step explanation:
Who cares? just copy down the answer.
(I'll be giving brainliest and extra points to who ever helps me!!)
Solve one and three fourths times two fourths.
A) fourteen sixteenths
B) fifteen sixteenths
C) seventeen sixteenths
D) eighteen sixteenths
Answers
Answer:
A. fourteen sixteenths
Step-by-step explanation:
[tex]1\frac{3}{4} x \frac{2}{4}[/tex]
[tex]\frac{7}{4} x \frac{2}{4}[/tex]
[tex]\frac{14}{16}[/tex]
Hope I helped you out!
~PumpkinSpice1
♥☼☺
Answer:
A it didnt let me answer at first and it dose now
Step-by-step explanation: