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.
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Related Questions
Anna and Hannah are reading the same book. At the beginning of the month, Anna was on page 29 and Hannah was on page 7. Anna will read 9 pages per day and Hannah will read 11 pages per day. Let
A
A represent the page of the book that Anna is on at the end of
t
t days into the month, and let
H
H represent the page of the book that Hannah is on at the end of
t
t days into the month. Write an equation for each situation, in terms of
t
,
t, and determine whether Anna or Hannah is farther along in the book after 14 days.
Answers
Answer:
Hannah
Step-by-step explanation:
Anna: Page 29 + number of pages read t days into the month
number of pages read t days in the month = 9 t times = 9 * t
Anna: 29 + 9t
Hannah: 7 + 11t using the same logic
14 days in: t = 14
Anna: 29 + 9*14 = 155
Hannah: 7 + 11 * 14 = 161
Hannah is further along
The equations for Anna's progress A = 29 + 9t and Hannah's progress H = 7 + 11t show that after 14 days, Hannah is farther along in the book with page 161 compared to Anna's page 155.
How to Apply Algebraic Equation?The equation we would write for each situation in terms of t are explained below:
For Anna:
A = 29 + 9t
For Hannah:
H = 7 + 11t
After 14 days:
For Anna: A = 29 + 9 * 14 = 29 + 126 = 155
For Hannah: H = 7 + 11 * 14 = 7 + 154 = 161
After 14 days, Hannah is farther along in the book as she is on page 161 while Anna is on page 155.
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Forty three fence posts are placed one yard apart. How many yards of fence is this?
Answers
Answer:
86
Step-by-step explanation:
43 x 2=86
#2: Find the value of X. (GEOMETRY)
I will give brainliest to BEST answer! fake answers will be reported.
refer to attachment!
Answers
===========================================================
Explanation:
Refer to the remote interior angle theorem (some books call it the exterior angle theorem). That says we can add the two interior angles and the sum is the exterior angle that is not adjacent to either interior angle.
(interiorAngle1) + (interiorAngle2) = exterior angle
(5x) + (2x+6) = 8x-11
7x+6 = 8x-11
6+11 = 8x-7x
17 = x
x = 17
----------------
Or the slightly longer method has you follow these steps:
y = missing interior angle in the upper right corner
The angle (8x-11) and angle y are supplementary
(8x-11) + (y) = 180
y = 180-(8x-11)
y = 180-8x+11
y = -8x+191
For any triangle, the three interior angles always add to 180
(angle1)+(angle2)+(angle3) = 180
(5x)+(2x+6)+(-8x+191) = 180
-x+197 = 180
-x = 180-197
-x = -17
x = 17
emliy is thinking of a number which she calls n she find 1/4 of the number and then subtracts 3. write an expressions that represents emlily number.
Answers
Answer:
1/4 n - 3.
Hope this helps, sorry if it doesn't.
find mLABC
is from Big Ideas
Answers
Answer: 50
Step-by-step explanation: add DBC and ABD to get 50 ABC is 50
Which set of ordered pairs has a range of {0, 1,4}?
А
(0, 0), (0, 1), (4, 1)
B
(0, 2), (1, 2), (4, 2)
с
(0, 0), (0, 1), (0, 2), (0, 4)
D
(-1,0), (0, 1), (2, 1), (3, 4)
Answers
Answer: А
(0, 0), (0, 1), (4, 1)
Answer:
D
Step-by-step explanation:
As you can see in the pic, range is the y-coordinate. C is not the answer bcs the range of C is {0,1,2,4}
Anna is working two summer jobs, making $18 per hour lifeguarding and making $11 per hour clearing tables. In a given week, she can work a maximum of 14 total hours and must earn at least $210. If Anna worked 12 hours clearing tables, determine the minimum number of whole hours lifeguarding that she must work to meet her requirements. If there are no possible solutions, submit an empty answer.
Answers
Answer: She would make $132 a day by cleaning tables for 12 hours and getting 11 per hour. She would have to get rid of 1 hour and 90 minutes of lifeguarding to get the same pay.
Step-by-step explanation:
Can someone plz help Me?
Answers
the answer to your question is C. 6^4
Answer:C? sorry if im wrong
Step-by-step explanation:
5 What rate of interest is paid on a deposit of $2000 which earns $400
interest in 5 years?
Answers
Answer:
4%
Step-by-step explanation:
Given
I = 400P = 2000R = ?T = 5 yearsFormula
I = PRTSolving.
I = PRT400 = 2,000 × R × 5400 = 10,000 × R400 / 10,000 = R0.04 = RChange 0.04 to percent
0.04 × 100 = 4%Answer:
4%Which decimal is 5.764 round to the nearest hundredth
Answers
Answer: I think it's 6
Step-by-step explanation:
the students printed 150 flyers to advertise their community dog show. jose posted 40%
Answers
Answer: what’s the full question??
Please answer this I am so bad at math
Answers
For triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.
We are given a triangle MNO.
We are also given that:
m ∠ MNP = 38°
m ∠ ONP = 39°
This clearly means that:
m ∠ MNP < m ∠ ONP
Also, since m ∠ MNP < m ∠ ONP , the sides opposite to the angles will also follow the same relationship.
Side opposite to ∠ MNP is MP
and side opposite to ∠ ONP is OP
so, the relation will become:
MP < OP
Therefore, we get that, for triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.
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The statements m MNP m ONP and MP < OP are true for triangle MNO.
A triangle MNO is presented to us.
Additionally, we learn that
m ∠ MNP = 38°
m ∠ ONP = 39°
This demonstrates that:
m, MNP, m, and ONP
The sides that are opposite to the angles will also adhere to the same relationship because m MNP m ONP.
MP is the side that faces MNP.
and OP is the side opposite to ONP.
hence, the relationship will be:
MP < OP
As a result, we understand that for triangle MNO, the assertions m MNP m ONP and MP OP are true.
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Can someone please help me with number 49? :D ty!
Answers
Answer:
The answer is 4.5 cups I hope this helps :D
Name the ray in TWO different ways.
M N P
Answers
PM
Assuming your n is on a side
Mr. Lamb is missing a solution for his next patient. He has a cylindrical test tube which is 4 cm across the inside. The depth of the tube is 9 cm. What is the volume of the cylinder in mL?
Answers
Answer:
V=113.04mL
Step-by-step explanation:
The question is asking us to find the volume of a cylinder in mL. For this, we can use the equation V=[tex]\pi r^{2} h[/tex].
We know the diameter, 4cm, and the height, 9cm.
In order to solve, we must first find the radius.
r=1/2d
r=1/2(4)
r=2cm
We can now plug this into our equation.
V=[tex]\pi r^{2} h[/tex]
V=[tex]\pi (2)^{2} (9)[/tex]
V=[tex](3.14)(2)^{2} (9)[/tex]
V=113.04mL
where is it located on the number line
Answers
move it 0.25 units right
Pls help i give 5 stars and crown
Answers
Step-by-step explanation:
10 %, 7/10 and 0.2 are the three numbers that add up to 1
0.1 + 0.7 + 0.2 = 1
Answer:
1/4 = 0.25
0.5
10% = 0.1
7/10 = 0.7
15% = 0.15
0.2
10% + 7/10 +0.2 = 1
You must write all your answers on one line:
Answers
Answer:
(A,1) (A,2) (A,3) (A,4) (B,1) (B,2) (B,3) (B,4)
Hope that helped?
write a polynomial function in standard form with the given zeros x=1,-1,-2
Answers
Answer:
y = x³ +2x² -x -2
Step-by-step explanation:
A polynomial with root q has a factor (x -q). The factored form of the polynomial is ...
y = (x -1)(x +1)(x +2)
y = (x² -1)(x +2) . . . . . . partial simplification
y = x³ +2x² -x -2
How i can answer this question
Answers
Answer:
A. 2(x+y+1). lmk if you need any more awnsers
(13-(4-1)-2)+4 Help I got finals and don't understand
Answers
Do the inner parentheses first
(13 - (3) - 2) +4
(13 - 3 - 2) + 4
(8) + 4
12
Hope this helps!
Brainliest is much appreciated!
Answer:
12
Step-by-step explanation:
( 13-3-2) +4
= 8 +4
=12
Li designed a survey to determine how comfortable students at her middle school are with fractions. There are 600 students in her middle school. The students are equally distributed among grade levels. She selected a sample of 28 students in her first-period class. Which best explains Li’s sample? random and biased random and unbiased nonrandom and biased nonrandom and unbiased.
Answers
Answer:
unbiased nonrandom
Step-by-step explanation:
By picking only people from 1st period they are not random.
They haven't said anything that would make these people biased.
Answer:
unbiased nonrandom
Step-by-step explanation:
I want quick plsssss
Answers
[tex]3 \times \frac{1}{2} \\ \\ = \frac{5}{2} [/tex]
PLEASE HELP!!!!
Simplify:
3x2 + 7xy + 9x + (-8xy) +21x2
Answers
Answer:
22 x ² − x y + 9 x
Step-by-step explanation:
The simplification is 24[tex]x^{2}[/tex] - x y + 9x and option E is correct
what is simplification?
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler (usually shorter).
simplify,
[tex]3x^{2}[/tex] + 7xy + 9x + (-8xy) + [tex]21x^{2}[/tex]
3[tex]x^{2}[/tex] + 21[tex]x^{2}[/tex] + 7xy - 8xy + 9x
24[tex]x^{2}[/tex] - 1xy + 9x
hence, the simplification is 24[tex]x^{2}[/tex] - x y + 9x and option E is correct
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Solve the system of equations
X=11+y
2x+y=19
Answers
Answer:
Step-by-step explanation:
To solve this system of equations, let's first find the value y. We can replace the x in the second equation with 11 + y, since we are told in the first equation that x is equal to 11 + y. So, let's replace x:
2(11 + y) + y = 19
22 + 2y + y = 19
22 + 3y = 19
3y = -3
y = -1
And look at that - we've found our y-value! Now, we can replace the y in the first equation with -1 to find the value of x.
x = 11 + (-1)
x = 10
So, the solution to this system of equations is (10, -1). Hopefully that's helpful!
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
B. 2
Step-by-step explanation:
1.87
11 x 17 / 100 = 1.87
18. A family drove 28 miles in 35 minutes. At that rate, how many minutes would it take the
family to drive 91 miles?
72.8 minutes
098 minutes
O 113.75 minutes
O 122.5 minutes
Answers
Answer:
Answer:
time = 113.75 minutes
= 113.75 min
= 01:53:45
= 1 hours, 53 minutes, 45 seconds
Step-by-step explanation:
50 POINTS!!! MUST BE CORRECT OR I WILL DELETE IT AND REPORT IT!
What is the solution to the equation –3 + 5x = 42?
Answers
Answer:
x=9
Step-by-step explanation:
-3 + 5x = 42
add 3 to both sides
5x=45
divide both sides by 5
x=9
Answer:
x=9
Step-by-step explanation:
BRO SOMEONE PLSS HELP ME
Write the inequality that represents the possible values for x
Answers
Answer:
6x + 12 < 10
Step-by-step explanation:
The side 10 is greater than 6x+12
PLEASE EXPLAIN!! I WILL GIVE BRAINLIEST TO WHOEVER EXPLAINS!
If the relationship is proportional, what is the missing value from the table?
–18
–15
15
18