The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
(image)
Which statement best describes a flaw in the student's proof?
Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.
Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.
Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.
Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
Answers
The statement that best describes a flaw in the students' proof is;
Option D; Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
From the given image, we can see that;
AB ≅ DC
Let us analyze each given option;
A) ∠DBC and ∠BDA are in the same triangle ΔBDC. Now, they can't be a pair of vertical angles because vertical angles are a pair of opposite angles formed when two lines intersect but this is not the case here.
They are also not alternate interior angles because alternate angles are formed when a transverse line intersects two coplanar lines and again that is not the case here.
B) In ΔABD and ΔBDC, we see that;
AB = DC. Also, by theorem of alternate interior angles, we can tell that;
∠ABD = ∠BDC
Similarly, ∠BDA = ∠DBC from alternate interior angles.
Thus, there is one corresponding side and two non-included angles which means the triangles are congruent by AAS Congruency postulate.
C) As seen in B above, this statement is correct because the triangles are congruent by AAS postulate.
D) Corresponding angles lie on the same side of the transversal. In this case, ∠BDA and ∠DBC lie on opposite sides and are even congruent by alternate interior angles.
Read more about congruency at; https://brainly.com/question/7727792
Related Questions
What is meant by a stratified sample?
Answers
Answer:
A stratified random sampling involves dividing the entire population into homogeneous groups called strata (plural for stratum). Random samples are then selected from each stratum. ... A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population.
Answer:
Sampling that is used to represent different groups depending on their different qualities.
Hope that helps. x
what is 7/8 x 4 ? ( 7/8 is a fraction)
Answers
Answer:
7/2 or 3 1/2
Step-by-step explanation:
7/8*4/1=28/8
Simplify= 7/2 or as a mixed fraction = 3 1/2
Hope this helps
Can I have the brainliest if I am right?
A tree trunk can be thought of as a cylinder with a height of 1.7 M if the tree trunk has a diameter of 60 cm what is its volume in metres cubed give your answer to 2 decimal place.
Answers
The formula for the volume of a cylinder is pi * radius squared * height, or πr^2h.
To find the radius of the cylinder, take the given diameter (60 cm) and divide it by 2. 60 / 2 = 30 cm.
Now we need to either find the height in centimeters or find the radius in meters. Because a centimeter is 1/100 of a meter, we multiply the radius by 100 to get the radius in meters.
We also must square the radius. So 30 cm multiplied by itself equals 900 cm.
Radius: 900 / 100 = 9 m
We have to square the radius before plugging it into the equation because it would mess up the numbers if we didn't (0.3 m squared is 0.09 m, which is very small).
Now we can plug these values into the formula for the volume of a cylinder.
π * r^2 * h = π * 9 m * 1.7 m = ~48.066 cubic meters
Rounded to two decimal places is 48.07 cubic meters.
The volume of the tree trunk is about 48.07 cubic meters.
Which expression is equivalent to 9x – 2x2 + 4x – x?
Answers
Answer:
-2x^2+12x
Step-by-step explanation:
Mandy has $2.25 credit on her mobile phone. It costs $0.10 to send a text message. What is the largest amount of text messages she can possibly send to her friends with $2.25?
Answers
Answer:
22.5
Step-by-step explanation:
since 2.25 divided by 0.10 is 22.5 so she can message 22.5 friends
Sierra left $17.75 as a tip for a waiter. This was 20% of the bill before the tip. How much was her total bill before the tip
Answers
Answer:
$31.95 Before tip.
Step-by-step explanation:
I believe you should just add 17.75+80%=31.95
Check: 88.75 x 0.2 = 17.75
Factorize (x-y)^2+(x-y)
Answers
..............answer..
Given that 372 × 68 = 25296 find the value of 3720 x 68
Answers
Answer:
252960
Step-by-step explanation:
3720 x 68 = 252960
hope it's helpful
[tex]3720 \times 68 = 372 \times 10 \times 68 = 372 \times 68 \times 10 = 25296 \times 10 = 252960[/tex]
1. 5 3/4 + 5/6 + 2 1/2
2. 3 1/3 - (5 - 1 5/6)
Answers
Holly spent a total of $28 to buy candy for his soccer team. He bought chocolate that cost $2 per bag and gummy that cost $3 per bag. There are 12 people on the team and each person only get one snack. x = bag of pretzel y = bag of chip
How many bars of chocolate did Holly buy?
Answers
Answer:
8 chocolate bars
Step-by-step explanation:
Elijah left his house at time zero and drove for 6 minutes to the store, at a speed of 1 blocks per minute. Then he stopped and went into the store for 6 minutes. From there, he drove in the same direction at a speed of 1 blocks per minute until he got to the bank, which is 3 blocks away from the store. He stopped at the bank for 7 minutes. Then he drove home at a speed of 3 blocks every minute. Make a graph of showing the number of blocks away from home that Elijah is xx minutes after he leaves his house, until he gets back home.
Answers
When plotting the graph, the times and distances Elijah drove are added
cumulatively on the horizontal and vertical axis of the graph.
Please find attached, the graph showing Elijah's distance from home in number of blocks, after he leaves his house.Reasons:
The distances travelled by Elijah in the given times are as follows;
[tex]\begin{tabular}{|c|cc|} \underline{Time}&&\underline{Blocks away from home}\\0&&0\\6&&6\\12&&6\\15&&9\\22&&9\\25&&0\end{array}\right][/tex]
Using the above table, a graph can be plotted with MS Excel insert Chart function, to plot a Scatter with Straight Lines and Markers chart.
Please find attached the required graph showing Elijah's distance driven in
number of blocks away from his house, in xx minutes after he leaves his
house, until he gets back home created with MS Excel.
Learn more about plotting graphs here:
https://brainly.com/question/371134
Answer:
the answer is 5 hours 6 minutes 2 seconds
Step-by-step explanation:
What two numbers multiplied together equal 42 but when added they equal -13
Answers
Answer: -7 and -6
Step-by-step explanation:
Complete all 4 problems
Answers
Answer:
7)-6a
8)7
9)x-1
10)8-k
Step-by-step explanation:
Here in every steps we took like terms to be added and finally there are no more like terms we cannot add nor subtract and we get answer
Answer:
7. -6a
8. 6x +5
9. x + 1
10. -k + 8
Step-by-step explanation:
7. A=1 1-7= -6 a - - 7a = -6a
8. 3x + 3x= 6x
6-1=5
6x+5
9. -8x + 9x = x
3-2 =1
x+1
10. 4+4 =8
k- 2k= -k
-k + 8
-453 divided by 15 = (simplest form)
Answers
Answer:
-453/15 = -30.2
Answer:
-30.2 or -30 1/5
Step-by-step explanation:
a *blank* *blank* trinomial has only one element in the solution set
Answers
Answer:
a solution set trinomial has only one element in the solution set
Step-by-step explanation:
Which expressions are equivalent to -2(2h+10)+4h
Answers
combine like terms that equals zero
so 20 is your answer
Tyee signed up for a streaming music service that costs $6 per month. The service allows Tyee to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Tyee have to pay in a month in which he downloaded 10 songs? How much would he have to pay if he downloaded ss songs?
Answers
Answer:
Total cost for 10 songs = 6 + [0.75 × 10]
= $13.5
Total cost for ss songs = 6 + [0.75 × ss]
Step-by-step explanation:
The land area of Connecticut is about 12,549,000,000 square meters. The land area
of Rhode Island is about 2,707,000,000 square meters. How many times greater is the land area of Connecticut than the land area of Rhode Island?
Answers
Answer:
4.636
Step-by-step explanation:
The ratio is the same when it is written in terms of billions of square meters:
CT/RI = 12.549/2.707 ≈ 4.636
The area of CT is about 4.636 times as large as the area of RI.
2. What additional Information What additional information do you need to prove ABC = DEF by the SSS Postulate?
AC = DF
AB = DE
BC = EF
Answers
We already know the other sides
Plz help ToT I'm horrible at math
Answers
Answer: 126
Step-by-step explanation:
A=2(wl+hl+hw)
Comparing Theater Sales
I need help A.S.A.P!!!
Answers
Step-by-step explanation:
oh come on ! you can see that with common sense : it is 2)
while the data itself is the same, but in figure B it is kind of suggested that "Super Cinema" had twice the sales of "Bud's Movies". which is not the case at all.
and that is one of the problems, when you don't show the whole data range (which happens when you don't start the data range at the actual beginning - like 0 in this case).
as I keep saying : never trust a statistic you have not falsified yourself ...
Fill in the table. What is the distance that David traveled going to his friend’s house and returning home?
Answers
Answer:12 and 12 hope this helps :)
Step-by-step explanation:
Answer:
mark her brialyist i cant spell lol
Step-by-step explanation:
HELP PLS!
I'm studying for UCAT as I want to get into medicine. I don't understand probability diagrams like these, please explain it to me.
Answers
Answer: 80 (choice B)
=========================================================
Explanation:
This is an interesting venn diagram. Each region is either a circle or some kind of arrow shape. The numbers in the regions correspond to the qualities mentioned. For example, the "55" in the circle outside the other arrow regions tells the reader that there are 55 secretaries who are reliable but don't possess any other quality. As another example, the 35 is inside the circle and the left-pointing arrow to tell us that there are 35 people who are reliable and organized.
What we want to find are the values that are in 3 or more regions. There's only two cases when this happens: The 15 and the 65 as they are in the circle, the double arrow, and one of the single pointing arrows. So we have 15+65 = 80 candidates that possess 3 qualities. No person has all four qualities because there isn't a value that's in all four regions at the same time. Or you could note that the left and right pointing arrows do not overlap which is a big clue that there's no way someone could possess all four qualities at once. It might help to trace out the figures using different colors so you can pull apart the four figures.
Write a function rule for "The output is three times the input increased by two
A) y=5x
B) y=3x+2
C) y=3x - 2
D) y=2x+3
Answers
X is the input.
Three times the input would be 3x
Increased by two would be adding two at the end.
Answer: B. y = 3x + 2
if the restaurant donated $690 to the soup kitchen what we’re the total sales for the day
Answers
Answer:
Total sales = x + $690
Step-by-step explanation:
x = amount of sales in a day
Donated amount = $690
Total sales = amount of sales in a day + Donated amount
Total sales = x + $690
High school
math/ geometry
Answers
Answer:
Well a triangle itself is worth 180 degrees (Inteirior angles)
your given “a” “b” and you need to find c.
So you can subtract
A is 50
B is 55
So
<BCA= 180- 55-50
Is the answer (b)
Answer:
B
Step-by-step explanation:
A triangle's angles all add up to 180 degrees. If m∠A is 50 and m∠B is 55 then m∠C is 75.
m∠C = 180 - (m∠A - m∠B); which is 180 - 105
180 - 105 is 75; Therefore, m∠C is 75 degrees
Proof: 50 + 55 + 75 = 180
calculate the volume of a cone with r=6.2 and h=10.9 and Pi=3.14
Answers
Answer: The volume(v) is 438.77.
Explanation: The formula for a right circular cone is in the image.
Two forces of 100 Newtons and 25 Newtons
act concurrently on an object. These two forces
could have a resultant force of
A) 0 N
B) 50 N
C) 100 N
D) 150 N
Answers
Answer:
100 N
Step-by-step explanation:
Use Pythagorean Theorm to solve:
a2 + b2 = c2
(100)2 + (25)2 = c2
10000 + 625 = c2
10625
Take the square root
c2= 100N
Your Answer: 100 N
carl ordered a refrigerator that weigh 192 pounds
Answers
Answer: good for him... how much did he spend on it?
subtract 3x-7x³+5x² from the sum of 2+8x²-x³ and 2x³-3x²+x-2
Answers
Answer:
(2 + 8 x^2 - x^3) + (2 x^3 - 3 x^2 + x - 2) - (3 x - 7 x^3 + 5 x^2) = 8 x^3 - 2 x
Step-by-step explanation: