Quadrilaterals Made Easy: Learn with Examples, Equations, and Expert Tips

Is there a congruence theorem that says that if three sides of two quadrilaterals are equal, then the two quadrilaterals are congruent?

Is there a rule for naming quadrilaterals in English? What I am expected to know about are: square, rhombus, rectangle, parallelogram, trapezium, kite. But how do we name other quadrilaterals?

Lines $CF,GE$ are parallel to diagonal $DB$.

Are the cyclic quadrilaterals $CBGDC,FBGDF$ (with same sides and angles) congruent? If not, how are they be described?

Two quadrilaterals are said to be similar if both of these two conditions satisfy:
Corresponding sides are proportional.
Corresponding angles are equal.
But in case of triangles, if any one of the above conditions is true then the other is also true and triangles are considered similar.
prove it or justify

Let $n>4$.
In how many ways can we choose $4$ vertices of a convex n-gon so as to form a convex quadrilateral, such that at least $2$ sides of the quadrilateral are sides of the $n$-gon?
Explain your answer, which should be expressed in terms of $n$.

In a convex quadrilateral $ABCD$, we have points $P\in <!--\; \in \; -->AB;R\in <!--\; \in \; -->AD$. Lines $PD$ and $RB$ intersect at a point $S$. Assume we can inscribe a circle in each of the quadrilaterals $APSR$ and $CDSB$. How do I prove that we can inscribe a circle in $ABCD$

1. translate and solve: three increased by twice a number is less than three times the difference of a number and five
2. translate and solve: negative two is less than or equal to one minus one-fourth of a number.
3. translate and solve: thirteen is greater than three minus ten times a number.
4.Joe is making a shower curtain. The pattern says that the curtain will use 5760 square inches. If the length is to be 72 inches, how wide will the curtain be?
5. the cost of the border material limits the circumference of a circular flower garden to 10 feet. What is the range of values for the diameter of the garden

The dimensions of a rectangular room are 12 feet 10 inches by 10 feet 1 inch. If square tiles of the same size are to cover the floor completely without any overlapping and if only whole tiles will be use, what is the largest possible length of a side of the tile?

There is a rectangular piece of land that will be used for landscaping. It is 22x30 ft. It has a 1 ft. wide trench that is on the inside of the rectangle, and runs along the edges (like a frame) throughout the inner perimeter. Also it has a 4 ft. deep excavation that will be used for planting. What is the cubic feet measurement of this rectangle?
As a side note the answers on the multiple choice test ranged between 300 to 400. Not any less or more. Please advise with solution. I am stumped. None of my answers come close. I understand the volume of a rectangle is LxWxH.

Compute the area (in Acres) of a rectangular parcel of land having length of 200.013 USft and width of 147.631 USft:
__________ acres

Rectangle ABCD, shown here, will be a golden rectangle if AB/AD=BC/BE where AE = AD. Let AE = 12 and find the ratio of AB to AD. (Round your answer to three decimal places.)

Definition #1: an isosceles trapezoid is a trapezoid with exactly one pair of parallel sides and whose none parallel sides are congruent.
Definition #2: an isosceles trapezoid is a trapezoid with one pair of parallel sides and with the other pair of sides congruent.
a) Explain how isosceles trapezoid are related to rectangles under each Definition?
b) How are these Definitions related to the Definition of trapezoid ?
c) a quadrilateral has vertices at (-a,0), (a,0), (b,c) and (d,c). Under Definition #1, what conditions must be b and d satisfy if the quadrilateral is an isosceles trapezoid ? Under Definition #2, what conditions must be b and d satisfy if the quadrilateral is an isosceles trapezoid ?
d) Are the two Definitions equivalent? why or why not?

Suppose $ABCD$ is a cyclic quadrilateral and $P$ is the intersection of the lines determined by $AB$ and $CD$. Show that $PA·PB=PD·PC$

The formula for finding the area of a trapezoid is $A=\frac{1}{2}(b_1+b_2)h$ where A represents the area of the trapezoid, $b_1$ and $b_2$ are based, and h represents the height. Solve for the formula for h.

There are $8$ line segments of lengths(in cm) $1,2,3,4,5,6,7,8$.How many quadrilaterals can be made with these line segments if circles can be inscribed in the quadrilaterals made?

You have two intersecting quadrilaterals (the area of intersection is the grey polygon with thick boundary):

These properties holds:
One quadrilateral is always a rectangle
There is always some intersection
Both quadrilaterals are convex (hence the intersection is a convex polygon as well)
The goal is to measure area of intersection (the actual shape is not needed, only a scalar showing how much space is covered by the intersection).

Prove that a 'tangential' quadrilateral (i.e. one with an in-circle) whose area is given by Brahmagupta's formula for a cyclic quadrilateral is also cyclic (and thus 'bicentric').