5.prove for kite abcd above that BD bisects both ABC and ADC
6.Given from what we now know from 5, prove that M must be the midpoint of AC
Answers
The kite is a quadrilateral that has two pairs of equal adjacent sides and
one of equal opposite angles.
5. The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] [tex]{}[/tex] Given
[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{AD}[/tex] = [tex]\overline{CD}[/tex] [tex]{}[/tex] Given
[tex]\overline{AD}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex] [tex]{}[/tex] By reflexive property
ΔABD ≅ ΔBDC [tex]{}[/tex] By Side-Side-Side, SSS congruency postulate
∠ABC = ∠ABD + ∠CBD [tex]{}[/tex] Angle addition postulate
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC
∠ABD = ∠CBD [tex]{}[/tex] Definition of congruency
[tex]\overline{BD}[/tex] is a bisector of ∠ABC [tex]{}[/tex] Definition of angle bisector
∠ADC = ∠ABD + ∠CBD [tex]{}[/tex] Angle addition postulate
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC
∠ABD = ∠CBD [tex]{}[/tex] Definition of congruency
Therefore;
[tex]\overline{BD}[/tex] is a bisector of ∠ADC [tex]{}[/tex] Definition of angle bisector
CPCTC is the acronym for Congruent Parts of Congruent Triangles are Congruent
6. The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
∠ABD ≅ ∠CBD [tex]{}[/tex] CPCTC (question 5)
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] [tex]{}[/tex] Given
[tex]\overline{BM}[/tex] ≅ [tex]\overline{BM}[/tex] [tex]{}[/tex] Reflexive property
ΔABM ≅ ΔCBM [tex]{}[/tex] According to Side-Angle-Side, SAS congruency rule
[tex]\overline{AM}[/tex] ≅ [tex]\overline{CM}[/tex] [tex]{}[/tex] CPCTC
[tex]\overline{AM}[/tex] = [tex]\overline{CM}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{AC}[/tex] = [tex]\overline{AM}[/tex] + [tex]\overline{CM}[/tex] [tex]{}[/tex] Segment addition postulate
[tex]\overline{AC}[/tex] = [tex]\overline{AM}[/tex] + [tex]\overline{AM}[/tex] = 2·[tex]\overline{AM}[/tex] [tex]{}[/tex] Substitution property of equality
[tex]\overline{AM}[/tex] = 0.5·[tex]\overline{AC}[/tex] [tex]{}[/tex] Division property of equality
M divides [tex]\overline{AC}[/tex] to two [tex]{}[/tex] Definition
M is midpoint of [tex]\overline{AC}[/tex] [tex]{}[/tex] Definition of midpoint
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Related Questions
Solve each inequality. Graph and check the solution.
e
1.
<3
2
0 1 2 3 4 5 6 7 8 9 10 11
Answers
Answer:
xxxx
Step-by-step explanation:
Express 405 1/3 in simplest radical form.
Answers
Answer:
3 cube root of 15
Step-by-step explanation:
theres your simple radical form
8(152/3) is 405 1/3 in simplest radical form.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
405 1/3 is equivalent to (405*3 + 1)/3 = 1216/3.
To express 1216/3 in simplest radical form, we can first simplify it by dividing both the numerator and denominator by their greatest common factor, which is 8.
1216/3 = (8*152)/3 = 8(152/3)
Now, we can see that 152/3 cannot be simplified any further, so the simplest radical form of 405 1/3 is: 8(152/3)
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I have more question
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Answer:
you would need three wholes because each whole would represent a loaf of pumpkin bread
Kendrick bought a laundry hamper online. It cost $9 plus 10% shipping and handling. What was the total cost?
Answers
Work Shown:
10% of $9 = 0.10*9 = 0.90
The shipping cost is $0.90, or 90 cents.
This means the total cost goes from $9 to $9.90
9*0.10=0.90
9+0.90=$9.90
a function is given, 2^x + 3. find f(-2)
Answers
Answer:
2_3_4_4/547767()9897568. thank
Which element should be used to help clarify a complicated idea in a text? (1 point) O a new topic O a bibliography O a visual O a research question w
Answers
The element which should be used to help clarify a complicated idea in a text is ; A research question.
According to the question;
We are required to determine which element should be used to help clarify a complicated idea in a text.A research question is the best fit which should be used to help clarify a complicated idea in a text.
This is so because; a research question provides a basis for accessing all perspectives there is to the complicated idea.
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Answer:
D
Step-by-step explanation:
how is this math? 0-0
simplify by expressing with radicals n√x^3^n
Answers
We can work with the exponents to simplify our expression, and we will get:
[tex]\sqrt[n]{x^{3n}} = x^3[/tex]
How to simplify the expression?Remember that a root of degree n is equivalent to an exponent of 1/n.
This means that we can rewrite a root of degree n as:
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
Then our expression:
[tex]\sqrt[n]{x^{3n}}[/tex]
Can be rewritten as follows.
[tex]\sqrt[n]{x^{3n}} = (x^{3n}})^{1/n}[/tex]
Now we have the exponent of an exponent, that means that we just need to take the product between the two exponents.
Now we can take the product of the exponents to get.
[tex]\sqrt[n]{x^{3n}} = (x^{3n}})^{1/n} = x^{3n*1/n} = x^3[/tex]
You can see that in the third step the exponents n and 1/n cancell eachother, so we end only with the exponent 3.
That is the expression simplified.
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On a family trip to Oman, Tarek drove 300 km in 5 hours. This is an example of a unit rate or a rate? Please tell the correct answer.
Answers
Answer:
300 km in 5 hours is the rate
unit rate is how much in one unit
in this case the unit is one hour
60km / hour
Which ratio is equivalent to the given ratio? 8: 16 Select each correct answer. 16/31 1/3 1/2 12/24
Answers
[tex]8:16\implies \cfrac{8}{16}\implies \cfrac{1}{2}\implies 1:2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{16}{31}\qquad \bigotimes~\hfill \cfrac{1}{3}\qquad \bigotimes~\hfill \cfrac{1}{2}\qquad \textit{\large \checkmark}~\hfill \cfrac{12}{24}\implies \cfrac{1}{2}\qquad \textit{\large \checkmark}[/tex]
Answer:
1/2. and 12/24
they are both halves just as the ratio is half of the given number
I need answers ASAP
Answers
Answer:
Simplifying
6r + r + -5r = 0
Combine like terms: 6r + r = 7r
7r + -5r = 0
Combine like terms: 7r + -5r = 2r
2r = 0
Solving
2r = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Divide each side by '2'.
r = 0
Simplifying
r = 0
7r-5r < this is the answer
6r+r=7r
Eve is going to buy 70 pens from either shop A or shop B.
Shop A : pack of 10 pens for £ 2.30
Shop B : pack of 5 for £ 1.60 buy 1 pack and get 1 half price .
What is the difference in cost for all 70 pens between the two shops ?
Answers
Answer: 0.70
Step-by-step explanation: Shop A: 2.20*7=15.40
Shop B: 7 packs with full price and seven with half
So, 1.40*7=9.80 and 9.80/2=4.90 is price of other seven
Take sum 9.80+4.90=14.70
So the difference between the two shops is
15.40-14.70=0.70 hope i helped have a good afternoon
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Answer:
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[tex](2\pi \:r {}^{2} ) \div 2[/tex]
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28.27
Given that X varies directly as Y³ and X = 54, Y = 3. find X 10 Y = 5 what is the relationship between X and Y?
Answers
Answer:
x=6y3
Step-by-step explanation:
we first find the constant of proportionality where by we say; x= ky3
we're given x = 54
and y = 3
so
54=k(3cubed)
therefore
54= 9k
divide be 9 both sides to get k which is the constant
k=6
now rewrite the equation replacing k with 6
it will be...
X=6Y3
A. Determine the value of each function
1. For p(x)=-2x + 5, determine:
a. p(5)
b. p(0)
c. p(-1/2)
Answers
Answer:
a= -5
b=5
c=6
substitue each value as x
Suppose we have a linear equation relating y and x defined by
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representation of y?
Select the correct answer below:
Answers
Answer:
(a) f(x) = -3x +6
Step-by-step explanation:
Solve for y, then write as a function.
3y +9x = 18 . . . . . . given
y +3x = 6 . . . . . . . . divide by 3
y = -3x +6 . . . . . . . subtract 3x
f(x) = -3x +6 . . . . . written using function notation
A bullet train can travel at 170 miles per hour. Will a graph representing distance in miles compared to time in hours show a proportional relationship? Explain
Answers
Answer:
yes
Step-by-step explanation:
the relationship between the hours and miles traveled is a direct relationship therefor would be able to be graphed as a linear function.
: Một khu đất 20 ha người ta trồng hai loại cây ngô và khoai. Năng suất của ngô tính theo x ha được (5-x/4) tấn trên 1 ha và năng suất của khoai tính theo y ha được (7-y/4) tấn trên 1 ha. Xác định diện tích trồng từng loại cây để sản lượng thu được là lớn nhất.
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Ernie deposits $9,800 into a pension fund. The fund pays a simple interest rate of 7%. What will the balance be after four years?
Answers
Answer:
$12,845.80
Step-by-step explanation:
take the first number and go +7%. repeat four times
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Answer:
Is a give number 4 5 is a reflexive property
answer this question fast
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Answer:
corona virus sjuwiwiwoe
Step-by-step explanation:
iaisowowow
All 5-digit zip codes in the United States are assigned by region. In Texas, all zip codes begin
with the number 7 while the second digit is restricted to numbers from 5 to 9. There is no
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4,000
5, 000
6, 000
7,000
Answers
Answer:
5,000
Step-by-step explanation:
[tex]\frac{1}{7}*\frac{5}{5-9} \frac{10}{0-9} *\frac{10}{0-9} * \frac{10}{0-9}[/tex]
Use the slope formula to determine the slope of the line containing the two points. Type your answer as an integer or reduced fraction in improper form if necessary.
Answers
Answer:
The slope is:
[tex] \binom{1}{2} [/tex]
In slope-intercept form the equation is:
[tex]y = \binom{1}{2} x - 3[/tex]
of the three lines in the graph one has slope m = 1 one has slope m = 2, and one has slope m = 1/5.
Put the lines in order from greatest to least slope.
Answers
Answer:
1/5 1 2
Step-by-step explanation:
given: AC is parallel to DF, m<1 = m<4
prove: AE is parallel to BF
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Answer:
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Step-by-step explanation:
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Find the x- and y-intercepts of the graph of -x+2y=6. State each answer as an integer or an improper fraction in simplest form.
Answers
The x-intercept is the point on the graph where it crosses the x-axis, and has coordinates of (a, 0), where a = x-intercept.
-x + 2y = 6
-x + 2(0) = 6
- x + 0 = 6
-x = 6
Divide both sides by -1 to isolate x:
-x/-1 = 6/-1
x = -6
Therefore, the x-intercept is (-6, 0), where its x-coordinate, a = -6.
Next, in order to solve for the y-intercept, set x = 0.
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b), where b = y-intercept.
-x + 2y = 6
-(0) + 2y = 6
0 + 2y = 6
2y = 6
Divide both sides by 2 to isolate y:
2y/2 = 6/2
y = 3
Therefore, the y-intercept is (0, 3), where its y-coordinate, b = 3.
PLEASE NEED THIS ASAP
Answers
Answer:
The answer is in the above attachment.
Which claim supports this graph?
A- Students Never use social media.
B- Students mostly use social media 0-3 times a day.
C- Students mostly use social media 8-11 times per day.
D- Students are not using social media enough.
Answers
Answer:
The answer is C.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
5. Aaron sold 126 boxes of cookies. This is 14 more than twice the
number of boxes his sister, Victoria, sold. How many boxes of
cookies did Victoria sell?
Answers
Answer:
112
Step-by-step explanation:
Aaron = y
Victoria = x
y = 14 +x
126 = 14 + x
x = 112
Victoria sold 112 boxes of cookies
1/5 divided by 2/3 input the answer as a fraction
Answers
Answer:
Three tenths/ 3/10
Step-by-step explanation:
1/5 divided by 2/3 is 0.3 which is equal to 3/10
$10.25 per hour x 25 hours round to the nearest cent
Answers
Answer:
256.25
Step-by-step explanation:
$10.25 not taxed x 25
