Given: PQ = RS; PQ|| RS
Prove: PQRS is a parallelogram
Answers
Answer:
If PQRS is a parallelogram, then — PQ ≅ — RS and — QR ≅— SP . If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then ∠P ≅ ∠R and ∠Q ≅ ∠S.
PQ=RS and PQ||RS implies PQRS is a parallelogram by showing that the diagonals bisect each other at O.
What is a parallelogram?
A quadrilateral with opposite sides equal and parallel but the angles are not right angle is called parallelogram.
Given that PQ=RS and PQ||RS .
Draw the parallelogram PQRS as in figure
To prove: PQRS is a parallelogram.
Construction: Join PS and QS as diagonals.
From the ΔORS and ΔOPQ,
PQ=RS (Given)
∠SOR=∠POQ (opposite angles)
∠PQO=∠OSR (since PQ=RS and PR is a traversal)
∴ΔOQS≅ΔOPQ
Hence, Op=OR and OQ=OS
Therefore , the diagonal of quadrilateral PQRS bisects each other.
Hence the given quadrilateral PQRS is a parallelogram.
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Related Questions
can someone please help me with this
Answers
Answer: 4?
Step-by-step explanation: 12 inches length times the 4 inches width = 48 square inches. but then you have to subtract the (22 times 2 = 44)
48-44=4???
A mustard seed has a mass of about 0.002 gram. A glass jar contains about 4.3602 x 10^4 A B C or D
Answers
Answer:
(2 x 10 ^-3) x (4 x 10 ^4)=8 x 10 ^1
Step-by-step explanation:
The mass of a single seed can be written as 0.002 = [tex]2*10^{-3}[/tex]
There are total of 4.3602 * 10 ⁴seeds in the jar
Total mass is the multiplication of these both numbers.
Since we want an estimate, we can use 4 instead of 4.3602 in the 2nd number.
The rule to multiply two numbers in scientific notation is:
[tex](a*10^{b} )*(c*10^{d} )=(a*c)*10^{b+d}[/tex]
So using this formula we multiply the 2 numbers and get answer as follows:
[tex](a*10^{b} )*(c*10^{d} )=(a*c)*10^{b+d} \\(2*10^{-3} )*(4*10^{4} )=(2*4)*10^{-3+4} \\=8*10^{1}[/tex]
1 .(+2)+(+8) 8. (4)-(4)
2. (+4)+(+8)
3. (1)+(+10)
4. (+11)+(11)
5. 0+(+9)
6. (+5)-(+10)
7. (12)-(+7)
Answers
Hello there! GraceRosalia is here to help! :)
(+2)=2
2+8=10
4-4=0
4+8=12
1+10=11
0+9=9
5-1-5
12-7=5
hope it helps
What is the slope of the line?
10
15
20
25
Answers
Answer:
Step-by-step explanation:
(10, 15), (20, 25)
(25 - 15)/(20 - 10) = 10/10 = 1
m = 1
Use mental math to find the missing factor.
33
,
000
÷
□
=
110
33
,
000
÷
□
=
110
A.
30
B.
300
C.
330
D.
3,000
Answers
B. is the answer just x
Answer:
thanks for telling me the answer
Step-by-step explanation:
have a bless day :)
A scale on a blue print drawing of a house shows that 10 centimeters represents 2 meters.What number of actual meters are represented by 18 centimeters on the blue print?
Answers
Answer:
1.4 centermeters
Step-by-step explanation:
if 2 centermeters is equal to 10 meters then divide 2 into 10 and come out to .5 so answer to 18 centermeters is 1.4
A line has a slope of 1/2 and contains the points (3, y) and (5,7). The value of y is.
Answers
Answer:
The value is 6
Step-by-step explanation:
Since the slope is 1/2, you can plot the coordinates 5,7.
5=x axis
7=y axis
After that you can use the formula rise/run = 1/2
Then you plot 3 on the graph. Then you use formula rise over run,
then you get 6
If MacCallum drives 325 miles in 5 hours, how far does he drive in 1 hour?
Answers
Answer:
65 miles in one hour
Step-by-step explanation:
MacCallum drove 325 miles in 5 hours so if you divide the amount of miles( 325) by the amount of hours to get to one, 5/5, you get 325/5=65/hour
A Baker's recipe uses for cups of water for every 9 cups of flour. Which ratio of cups of water to cups of flour will make the same recipe?
Answers
Answer:
It would be 4 to 9 or 4/9!
Step-by-step explanation:
Given any right triangle, the sum of the areas of the squares formed by the legs is equal to the area of the hypotenuse. This is referred to as the:
Question 5 options:
A) pythagorean theorem
B) perimeter
C) surface area
D) area
Answers
Explanation:
You are probably familiar with the formula [tex]a^2+b^2 = c^2[/tex] which is the pythagorean theorem.
The [tex]a^2[/tex] is the square of the first leg 'a', while [tex]b^2[/tex] is the square of the second leg b. Adding those two squares leads to the square of the hypotenuse c, aka [tex]c^2[/tex]. This only works with right triangles, which are triangles that have a 90 degree angle.
2. Select all transformations that must take any point A to any point B.
A. Rotation of 180° around A
B. Rotation of 180°around B
C. Rotation of 180° around the midpoint of segment AB
D. Reflection across the line AB
E. Reflection across the perependicular bisector of segment AB
F. Translation by the directed line segment AB
G. Translation by the directed line segment BA
Answers
The given transformation of reflection, rotation and translation are rigid transformation
The transformation that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment ABReflection across the perpendicular bisectorTranslation by the directed line segment ABReason:
Question: The given quadrilaterals ABCD and A'B'C'D' are congruent
Required; To select all transformation that must take a point A to point B
Solution:
Rotation of 180° around the midpoint of segment ABA rotation of 180° about the midpoint of segment AB will change the places of points A and B
A(x, y) → R₁₈₀ → A'(-x, -y)
Let the coordinates of the origin be the midpoint of segment AB, and let (x, y) represent the coordinate of the point B(x, 0) we have;
∴ The coordinates of point A is A(-x, 0), which gives;
A(-x, 0) → R₁₈₀ → A'(x, 0) = point B
Therefore a rotation about the midpoint of AB must take point A to point B
Reflection across the perpendicular bisectorThe reflection of a point (x, y) about y-axis gives a point (-x, y), therefore, we have;
A(-x, 0) → Reflection across the y-axis → A'(x, 0) = point B
Therefore, a reflection across the perpendicular bisector of the line AB must take the point A to point B
Translation by the directed line segment ABA translation along the directed line segment AB of point A(-x, 0) 2·x units right gives;
A'(-x + 2·x, 0) = A'(x, 0) = Point B
Therefore, the transformations that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment AB
Reflection across the perpendicular bisector
Translation by the directed line segment AB
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2/9 divided by 5/12
simplest form
the answer is a fraction
Answers
2/9 times 12/5 = 24/45
simplify that you get 8/15
The solution in form of fraction is,
⇒ 8 / 15
We have to given that,
An expression to solve,
⇒ 2/9 divided by 5/12
Now, We can divide the numbers into form of fraction as,
⇒ 2/9 ÷ 5/12
⇒ 2/9 × 12/5
⇒ 24 / 45
⇒ 8 / 15
Therefore, The solution in form of fraction is,
⇒ 8 / 15
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x + 3 + x - 8 + x = 55
x = ?
Answers
Answer:
x=30
Step-by-step explanation:
isolate the numbers that don't contain the variable, then divide the factors that don't contain the variable.
Answer:
x=20
Step-by-step explanation:
Given: x+3+x-8+x=55
Combine like terms: 3x-5=55
Add 5 to the other side: 3x=60
Divide both sides by 3: X=20
How do you write 0.27777777777777..... as a whole number
Answers
Answer:
i think 27777777777777/100000000000000
Step-by-step explanation:
Answer:
Convert it to a whole number
Step-by-step explanation:
by multiplying it with 1000000000000
=2.78 x 10 ^ -15
What value of x would make the value of the expression 0? −10+11+x
Answers
Answer:
x=-1
Step-by-step explanation:
-10+11+x=0
-11 -11
-10+x=-11
+10 +10
x=-1
(7, 4), (5, - 1), (3, - 8), (1, - 5), (3, 6)
Determine whether the relation is a function. Explain pls
Answers
Answer:
The given relation is not a function.
Step-by-step explanation:
A relation is any set of ordered pairs, which can be thought of as (input, output).
A function is a relation in which no two ordered pairs have the same first component (x-values or input) and different second components (y-values or output).
Given the following relation: {(7, 4), (5, - 1), (3, - 8), (1, - 5), (3, 6)}
There is an input value (x = 3) that has two corresponding outputs (y-values): y = -8 and y = 6.
Remember that a function can only take on one output for each input.
It also helps to do the Vertical Line Test, which allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. To use the vertical-line test, imagine dragging a ruler held vertically across the graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value.
Attached is a screenshot of the plotted points on a graph, where I performed the Vertical Line Test. The green line is the vertical line that contains two points that made the relation invalid as a function.
Please mark my answers as the Brainliest if you find my explanation helpful :)
solve the quadratic by completing the square x^2-10+18=0
Answers
Answer:
Data set: 47, 45, 44, 41, 48
1. Find the mean.
Mean = 47 + 45 + 44 + 41 + 48
5
= 225
5
= 45
2. Find each absolute deviation.
Absolute deviations: 2, 0, 1, 4, 3
What is the mean absolute deviation (MAD) for the data set?
MAD =
Step-by-step explanation:because thats it because yea
what is the answer to (-15)− (2)x(-10+(+3)?
Answers
Answer:
-1
Step-by-step explanation:
-15-2(-7)
-15+2·7
-15+14
-1
I dunno how to do this
Answers
Answer:
2z-4
Step-by-step explanation:
Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!
Answer:
2 − 4 Is the correct answer
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
Fill in the missing number. % of 60 = 24
Answers
Answer:
40%
Step-by-step explanation:
Step 1: Set up an equation.
[tex]\frac{x}{100}(60)=24[/tex]Step 2: Simplify both sides of the equation.
[tex]\frac{x}{100}(60)=24[/tex] [tex]\frac{60}{100}x= 24[/tex] [tex]\frac{3}{5}x=24[/tex]Step 3: Multiply both sides by 5/3.
[tex]\frac{3}{5}x* \frac{5}{3}=24 * \frac{5}{3}[/tex] [tex]x = \frac{120}{3}[/tex] [tex]x = 40[/tex]Therefore, the missing number is 40 to make 40% of 60 = 24.
If x = 4 and y = 7, evaluate the - following expression: 20 +2(3y - 4x)
Answers
Answer:
30
Step-by-step explanation:
20+2(3*7 - 4*4)
20+2(21-16)
20+2*5
20+10
30
Please help! Simplify and know whether these examples are equal. Picture above.
Answers
Answer: -9/4
Step-by-step explanation:
https://www.symbolab.com/solver/equation-calculator/%5Cfrac%7B%5Cfrac%7B%5Cfrac%7B3%7D%7B5%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B-%5Cfrac%7B4%7D%7B5%7D%7D?or=input
Find the slope of the line formed by connecting the points:
(-5, 4) and (5,1).
Answers
Answer:
The formula you will want to use is y(2) - y(1) over x(2) over x(1).
Basically, the Y variables (4 and 1) will be subtracted from each other. Aka, 1-4, which is -3. You put that over 5-(-5) or (5+5) which is 10. Now you have -3/10.
Find UV. This is Geometry. Help
Answers
So,
(2x12) - 22 = UV
24-22 = UV
UV = 2
the length of a side of a rectangle is 6 cm. what should the length of the other side be so that the perimeter of the rectangle is smaller than the perimeter of a square with a side of 4cm?
Answers
Answer:
1cm
Step-by-step explanation:
A square with a side of 4cm will have a perimeter of 16cm (4+4+4+4).
If you put 2 on the other side of the rectangle, the perimeter will be: 6+1+6+1=14cm, which is smaller than the square's perimeter.
refers to an endless number of terms that follows a sequence and end with ellipsis
Answers
I hope it helps
Please help ASAP giving lots of points to the best and most helpful answer I don’t care if it’s just the answer I don’t need an explanation thanks
Answers
Answer:
Terms Are
8 , 16 , 32
5 , 10 , 15 , 20
3 , 6 , 12
All of them are less than 50.
Step-by-step explanation:
[tex]\left(\sqrt{2}+1\right)\left(5+\sqrt{2}\right)[/tex]
Answers
[tex]( \sqrt{2} + 1)(5 + \sqrt{2}) \\ = \sqrt{2} (5 + \sqrt{2} ) + 1(5 + \sqrt{2} ) \\ = 5 \sqrt{2} + 2 + 5 + \sqrt{2} \\ = 7 + 6 \sqrt{2} [/tex]
Answer:7 + 6√2
Answer:
[tex]\huge\boxed{\sf 7 + 6\sqrt{2}}[/tex]
Step-by-step explanation:
[tex](\sqrt{2} +1)(5+\sqrt{2} )\\\\= \sqrt{2} (5+\sqrt{2} )+1(5+\sqrt{2} )\\\\= 5\sqrt{2} + (\sqrt{2})^2+5+\sqrt{2} \\\\= 5\sqrt{2} + 2 + 5 + \sqrt{2} \\\\= 2+5+\sqrt{2} + 5\sqrt{2} \\\\= 7 + \sqrt{2} (1+5)\\\\= 7 + 6\sqrt{2} \\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807why am i so stressed can someone answer me
Answers
These Are some reasons why are you stressed :
Mental health conditions, such as depression, or a building sense of frustration, injustice, and anxiety.
Answer:
Its highschool its stressful
Step-by-step explanation:
What is the answer to 18-6×=162 when
worked out?
Answers
Answer:
If you mean 18-6x=162
18-6x=162
-6x=162-18
-6x=144
divide both sides by -6
x=-24