What is Parallelogram: Definition and 126 Discussions
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English.
The three-dimensional counterpart of a parallelogram is a parallelepiped.
The etymology (in Greek παραλληλ-όγραμμον, parallēl-ógrammon, a shape "of parallel lines") reflects the definition.
I understand that I can divide this shape into a few parallelograms and a triangle and calculate the center of mass of each, but am confused as to what I should do after that. My physics teacher also wants us to use integrals, but I'm assuming I can calculate the COM of each parallelogram and...
https://mathhelpboards.com/threads/3-coordinates-of-parallelogram-stuv.6195/
this problem had over 6000 views so I was interest in posting it to Linkedin hoping it would recruit some new members
however it had a graph in the OP which has been deleted but another was posted using some code...
Chapter 1, Section 1.1.
Look at the picture. Question 57.
Let me see.
To show this prove, I must find the midpoint of the diagonals. The midpoint of (b, c) and (a, 0) must be the same as the midpoint of (0, 0) and
(a + b, c).
You say?
Hello, we are learning about similar triangles and this was a problem. So I know that opposite sides of a parallelogram are congruent as are opposite angles, so I can establish similarity with triangles WYS and STW, but I don't understand how that proves SX x YW = SV x WT because the proportions...
In parallelogram $ABCD$, $\angle B$ and $\angle D$ are acute while $\angle A$ and $\angle C$ are obtuse. The perpendicular from $C$ to $AB$ and the perpendicular from $A$ to $BC$ intersect at $P$ inside the parallelogram. If $PB=700$ and $PD=821$, find $AC$.
Hi,
I have been learning about Laplace's equation recently, and have been wondering: how would we approach the problem if the region was a parallelogram (or some other shape that isn't a standard rectangle or circle)? Is this something that could feasibly be solved by hand, or would it require...
Hi, I work as a math/science tutor, and a student had this question. He said you're supposed to find the values of x, y, and z and the only information given is that it is a parallelogram.
It looks like it might be under-determined to me, every equation I write for it ends up reducing to
15x...
I tried to mess around with some equations in Mathematica with more or less success. Let's call ##a,b## the two sides and ##\delta## the angle between them. I contructed vectors that point to the corners of the room.
##\vec{a} = (0, 0)##
##\vec{b} =(a, 0)##
##\vec{c}=(a+b \cos{\delta}, b...
Through symmetry of parallelogram,I have come to this:
Here 1,2,3,4 denotes the area of the particular regions.Then I am stuck.Please help what to do next or whether there is any other way.
Basically the altitudes of a parallelogram have two lengths, 8 and 10 and they intersect at an angle whose sine is 1/4. I'm attempting to find the area of the parallelogram.
I'm having trouble creating a good picture of it. Seeing if I could receive some help, thanks!
How does the parallelogram method work to solve one of two forces with different angles? Or better said, how do you derive the method so that I can get a better understanding of it ?
The diagonal divides the parallelogram into two triangles, each triangle circumference is 6.21 m. The circumference of the parallelogram is 7.12 m. Calculate the diagonal length.
I need tips how to solve this problem.
In an ABCD.EFGH cuboid with AB = 4 cm, BC = 3 cm, and CG = 5 cm there is a parallelogram OBFPH with O is located at the center of ABCD and P is located at the center of EFGH. The distance between the lines HO and PB is ...
A. 5\sqrt3 cm
B. 5\sqrt2 cm
C. \sqrt5 cm
D. \frac{5}{2}\sqrt2 cm
E...
Homework Statement
u and v are two vectors in the same plane.
Vector OM = u+2v
Vector OP = 6u+v
Vector OQ = 5u +2v
Vector OR =2(VecOM) +v
Given that ZPQM is a parallelogram, express Vector OZ in terms of u and v.Homework EquationsThe Attempt at a Solution
First they wanted me to find Vectors...
Homework Statement
Find the area of Parallelogram ABCD where AD=4 and CD=6 and angle ABC=125 degrees, tell whether the area is greater than 24 or not?
See the attached picture
Homework Equations
Area of Parallelogram = length * breadth
The Attempt at a Solution
Sol: 4 * 6 = 24
but answer is...
One way to see that spacetime is curved is to try and draw a "rectangle" in spacetime (see the figure in the Feynman lectures, ch 42.7): If I wait for 100 seconds and then move upwards on earth, I end up at a different point in spacetime than when I first move upwards and then wait for 100...
Homework Statement
The coordinates of the parallelogram ABCD are:
A (-2; 1)
B (5; 2)
C (6; 5)
D (-1; 4)
We also know that the diagonals intercept in the middle of each other (so if the diagonals are AC and BD, and the intercept in point M, then AM = MC, and BM = MD). Not sure if this...
Hello, could someone please help me with this question? I don't even know where to begin.
Given vectors a = (2, x, 0), b = (1, 0, −1) and c = (5, −9, 3), and let P(2, 1, −1)
be a point. Find the value of x in a such that the angle between a and b is π/4, then find the area of parallelogram...
$\tiny{s6.793.12.4.27}$
$\textsf{area of a parallelogram with adjacent sides}\\$
$\textsf{$\vec{P}{Q}$ and $\vec{P}{R}$ is the length of this cross product:}$
\begin{align}
|PQ \times PR|&=\sqrt{()^2+()^2}=
\end{align}
$\textit{new on vectors...
not sure what goes into $()^2$}$
Workings
$\triangle ADE \cong \triangle CFE \left(AAS\right)$
$\angle AED = \angle CEF $( vertically opposite angles )
$\angle CFE= \angle EDA $( alternate angles )
$AE=EC $( E midpoint )
$ii.$ADCF is a parallelogram because diagonals bisect each other.
Where is help needed
How should...
Homework Statement
23. In a ABCD quadrilateral let P,Q,R,S be midpoints of sides AB,BC,CD and DA. Let X be the intersection of BR and DQ, and let Y be the intersection of BS and DP. If ##\vec{BX}=\vec{YD} ## show that ABCD is a parallelogram .
Homework Equations
## (\vec{a}\cdot\vec{b})=0##...
ABCD is a parallelogram . X is the midpoint of AD & Y is the midpoint of BC. Show that the area of $\triangle {ABX}$ is $\frac{1}{4}$ the area of ABCD
Can you help me with this proof ? were should i start ? I think It should be by proving
$\triangle{DBC} \cong \triangle{DBA} $ using SAS as...
Acording to this diagram vector P = vector BC and vector Q = vector OB(their magnitudes are also respectively equal.)
Therefore acoording to the congruency of triangles angle alpha = (theta)/2. But this is not right( what's wrong )
{Tan(alpha) = Qsin(theta)/(P + Qcos(thets)) ]
Why resultant...
I'm curious if it looks like I defined the reasons correctly to prove that FBCD is indeed a parallelogram. Specifically, I'm unsure if I'm using #4 "definition of coincident" and #5,6 "reflexive property" correctly in their terminology. I don't have anyone else, or any teacher to ping this...
I believe I could work this problem fine had the instructor not placed statements #3,4, and 6, as well as the reasons # 5 and 7. I can't seem to understand where he's using the transitive property in #5. If these steps weren't here I would assume, I'm only using substitution to prove that "RS"...
A parallelogram exists within a rectangle which measures 15 inches tall by 20.5 inches wide.
A=15 inches
B=20.5 inches
C=1.5 inches
(C makes a 90° angle with X)
Solve for lengths X and Y and angle Z of the parallelogram and please tell me how you did it!
Homework Statement
If the area of a rectangular field has length of 110 m and 80 m.If a spaceship is traveling with 0.9c velocity along the diagonal of the field.Then what is the area of the field seen by the astronaut in the spaceship?
Homework Equations
L=L(initial) Root over (1- (v/c)^2)...
Hi there,
I'm doing a bit of amateur scale model making as a hobby, building shapes out of flat-cut pieces. Trigonometry is a huge help with this, but I've hit a snag where I'm trying to calculate the angle of a particular parallelogram so it fits with the rest of the geometry.
1...
Homework Statement
This question has popped up recently and I was completely stumped. How to find the angles of a parallelogram given only area and the length of the diagonals? I'm trying to find a generic solution or formula that works for a non-rhombus.
Homework EquationsThe Attempt at a...
Homework Statement
Find the coordinates of the vector of the height of the parallelogram formed by vectors a={1, 2, 1} and b={2, -1, 0}
Homework Equations
A=|axb|, A=|a|*h
The Attempt at a Solution
I can find the intensity of the vector h i.e the length of the height, but not its vector. I...
$\textbf{Problem:}$
Let $T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be the linear transformation that reflects each point through the $x_2$ axis. Make two sketches that illustrate properties of linear transformation.
$\textbf{Solution:}$
Let $T(\textbf{x}) = \begin{bmatrix} -1 & 0 \\ 0 & 1...
$\textbf{Problem}$
Let $\textbf{u}$ and $\textbf{v}$ be vectors in $\mathbb{R}^n$. It can be shown that the set $P$ of all points in the parallelogram determined by $\textbf{u}$ and $\textbf{v}$ has the form $a\textbf{u} + b\textbf{v}$, for $0 \le a \le 1, 0 \le b \le 1$. Let $T: \mathbb{R}^n...
I'd really need help with this. Thanks.
1. Homework Statement
Draw a parallelogram:
a = 4cm
e + f (diagonals) = 11cm
angle between a and e = 22°
Homework Equations
2 and 2 sides are parallel
both diagonals halve each other
(diagonal e goes from A to C)
The Attempt at a Solution
(attachment)
Can anyone help me set this problem up?
I am trying to figure out how to Prove the Sander's Parallelogram.
See it here:
http://www.tigel.nl/fun/files/opticals/Ill...ith_line-25.htm
basically it is proving that the bisectors are of equal length
The question is: what would be needed...
I am working on a task right now. I am currently trying to find the area of a parallelogram. I do not have the height. I only have the dimensions. I have tried suggestions like dividing the parallelogram into triangles and doing 1/2bh. The dimensions I have are the 1/2,1/2,\sqrt{2}/4...
Homework Statement
Find the are of the parallelogram ABCD where A is (1,2,-3), B is (-1,3,-4) and D is (1,5,-2)Homework Equations
Area=\left|AxB\right|
where A and B are the vectors AD, and AB respectively.The Attempt at a Solution
I have calculated AD to be= (0,-3,-1)
and AB=(2,-1,1)
∴ to...
Why is the parallelogram rule for the addition of forces as it is?
I feel it must have some deep origin and pointing to something fundamental. Though I know this problem may have no answer: God design it as such.
But I wonder how the first person came up with this rule, where does his/her...
Homework Statement
Let P, Q, and R be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vector S.
P (2, 0 ,-1), Q (-2, 4, 1), R (3, -1, 0)
Homework Equations
PR = QS
PQ = RS
The Attempt at a Solution
I took the two equations and solved both of them...
(a) $\vec{ST} = \pmatrix{9 \\ 9}$
so $V=(5,15)-(9,9)=(-4,6)$
(b) $UV = \pmatrix{-4,6}-\lambda \pmatrix{9,9}$
(c) eq of line $UV$ is $y=x+10$ so from position vector
$\pmatrix{1 \\11}$ we have $11=1+10$
didn't know how to find the value of $\lambda$
(d) ?
Homework Statement
In the parallelogram ABCD the internal bisectors of the consecutive angles B and C intersect at P. Use vector method to find angle BPC.
Homework Equations
The Attempt at a Solution
I assume angle BPC to be θ and the point of intersection of internal bisectors to be P...
I can find the area of the parallelogram when two adjacent side vectors are given. But how to find the area of the parallelogram when diagonals of the parallelogram are given as
\alpha = 2i+6j-k and \beta= 6i-8j+6k
Homework Statement
"Find the area of a parallelogram defined by the two vectors P=(4,-10,3) and Q=(2,1,0)"
Homework Equations
The area of the parallelogram is equal to the magnitude of the cross product of the two vectors? i.e. Area = |PXQ|
The Attempt at a Solution
PXQ =...