Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [quadrilateral]

For questions about general quadrilaterals (including parallelograms, trapezoids, rhombi) and their properties.

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Squares, rectangles, rhombi, parallelograms and trapezoids are special kinds of quadrilaterals.

672 questions
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In a parallelogram, does the diagonal bisect the angles that they meet?

I understand the following properties of the parallelogram: Opposite sides are parallel and equal in length. Opposite angles are equal. Adjacent angles add up to 180 degrees therefore adjacent angles are supplementary angles. (Their sum equal to…
Ridhwaan
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What shape is this quadrilateral?

It is a quadrilateral but I do not know which one it is:
user401521
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How do I know if this quadrilateral is cyclic?

There are some pairs of angles that are equal to each other, but none of the values are known.
shurup
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Value of one angle of a quadrilateral, when three sides are quadrilateral are given

In quadrilateral $ABCD$, $AB=BC=CD$. The value of $∠BAC$ is $40º$ and the value of $∠CAD$ is $30º$ what is the value of $∠ADC$?
Rangan Aryan
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How to know if a quadrilateral is circumscribed

Let's say I have a quadrilateral that is convex and I know the points that are forming it. How can I know if the quadrilateral is circumscribed? Is it true that a quadrilateral is circumscribed if and only if the sum of opposite sides are equal? In…
Copacel
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Area of an irregular quadrilateral.

An irregular quadrilateral has lengths $1, 4, 7$ and $8$ units. What is the maximum area of the quadrilateral possible? To find the area of an irregular quadrilateral, five values are needed; four sides along with an angle or the size of at least…
Math Tise
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Finding the fourth vertex of a quadrilateral of given area

Having the three vertices of a quadrilateral of given area, how can I obtain the coordinates of the fourth vertex? I have used the following formula which gives the quadrilateral area: $$A = \frac12 |(x_4-x_2)(y_1-y_3) +…
Mehdi
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Finding Area of a Quadrilateral

Can someone please help me through this problem? I am not even really sure where I should start. Quadrilateral ABCD has vertices A(-2,-2), B(1,4), C(8,4), D(5,2). Find the area of the quadrilateral, round your answer to the nearest tenth if…
IHeartBunnies
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Finding $PR + RQ$ given $PQ = 1$

Suppose we have triangle $ABC$ such that $\angle B$'s external angle bisector intersects $AC$'s extension at $P$ and $\angle A$'s external angle bisector intersects $BC$'s extension at $Q.$ Then, let the intersection of $BP$ and $AQ$ be $R.$ If the…
questionasker
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Orthographic projection

A quadrilateral $ABCD$ is given, $AD=BC$. The projections of $AD$ and $BC$ on $AC$ are equal. Is $ABCD$ parallelogram? Let $DD_1\perp AC$ and $BB_1\perp AC$. We have $AD_1=CB_1$. I found that the triangles $\triangle AD_{1}D$ and $\triangle…
Knowledge Greedy
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Prove quadrilateral ABCD is a parallelogram

enter image description here In the image, EFGH is a parallelogram, and BE=HC=GD=AF. Can I prove that ABCD is also a parallelogram?
logic
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Area of a right quadrilateral

Quadrilateral $ABCD$ has right angles only at vertices $A$ and $D$. The numbers show the areas of two of the triangles. What is the area of $ABCD$? The rectangle $DABC'$ will have an area of $30$. I am not sure how to proceed after that. Can…
Hari
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How to find inner angles and side of the rhombus given height and diagonal AC

I have to find inner angles $\alpha$, $\beta$, $\delta$ and $\gamma$, other diagonal $\left|BD\right|$ and length of a side $a$ into a rhombus where is given the height $h = 2\sqrt{3} cm$ and the diagonal $\left|AC\right| = 4\sqrt{3} cm$. How would…
andrej benedičič
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Permutation polygon

How can we calculate the number of ways in which a $p$-sided polygon can be made inside a $n$-sided polygon such that no side of the $p$-sided polygon is in common with the $n$-sided polygon?
imposter
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Maximum value of largest side

If we have a quadrilateral with integral and distinct sides and second largest side is 10 then the value of largest side is? And, we can solve it by saying that other two sides will be 9 and 8 respectively {because the other two sides are distinct…
tapus aggarwal
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