Why study quadrilaterals?

Kwenze0l
2022-09-04
Answered

Why study quadrilaterals?

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Mario Monroe

Answered 2022-09-05
Author has **12** answers

As a mathematician who just had to redo his kitchen floor due to water damage, I can tell you that my knowledge of quadrilaterals came in really handy. I had to measure and cut pieces of laminate flooring to fit quite exactly around corners which were generally not square.

asked 2022-11-29

All rectangles are squares, but not vice versa. True oe False

asked 2022-11-24

Which quadrilateral is equiangular but not equilateral.?

asked 2022-11-28

When using a series of squares that are exactly the same shape, implied depth can be achieved byalternating value

a. relative size

b. overlapping

c. relative position

d. all of these answers

a. relative size

b. overlapping

c. relative position

d. all of these answers

asked 2022-07-22

Suppose $ABCD$ is a cyclic quadrilateral and $P$ is the intersection of the lines determined by $AB$ and $CD$. Show that $PA\xb7PB=PD\xb7PC$

asked 2022-08-22

As in the following figure of a quadrilateral;

If the diagonals are stated to bisect each other, I thought this should hold (considering the bottommost triangle in blue lines);

$\frac{\overrightarrow{a}+\overrightarrow{b}}{2}+\frac{\overrightarrow{b}-\overrightarrow{a}}{2}=\overrightarrow{b}$

But this shows that all quadrilaterals have their diagonals bisecting each other, since this gives $\overrightarrow{b}=\overrightarrow{b}$ , which implies it's true for all $\overrightarrow{a}$ and $\overrightarrow{b}$. Which obviously isn't true.

Where did my reasoning go wrong?

If the diagonals are stated to bisect each other, I thought this should hold (considering the bottommost triangle in blue lines);

$\frac{\overrightarrow{a}+\overrightarrow{b}}{2}+\frac{\overrightarrow{b}-\overrightarrow{a}}{2}=\overrightarrow{b}$

But this shows that all quadrilaterals have their diagonals bisecting each other, since this gives $\overrightarrow{b}=\overrightarrow{b}$ , which implies it's true for all $\overrightarrow{a}$ and $\overrightarrow{b}$. Which obviously isn't true.

Where did my reasoning go wrong?

asked 2022-07-24

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?

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?

asked 2022-08-18

This is a question from Kiselev's plane geometry book:

Four points on the plane are vertices of three quadrilaterals. Explain how this happens.

How do you explain this?

Four points on the plane are vertices of three quadrilaterals. Explain how this happens.

How do you explain this?