MHB True/false units,amounts of plane figures

[Petrus]

Consider the following amounts of plane figures: A = {All squares}, B = {all diamonds}, C = {all rectangles}, D = {all parallelograms}, E = {all trapezoidal with three equal sides}, F = {all trapezoidal with at least a straight corner angle}. Examine which of the following statements are true. Reply with the letter R (true) or F (false).
__________ (a) B U C= D
__________ (b) D ∩ F= C
__________ (c) D ∩ E= B
_________ (d) F "subset" D U E
__________ (e) E ∩ F= B ∩ C

Any advice?

 

[soroban]

Hello, Petrus!

Examine which of the following statements are true.
Reply with the letter T (true) or F (false).

__________ (a)
__________ (b)
__________ (c)
__________ (d)
__________ (e) Any advice?

Yes . . . Give us the statements!

 

[Petrus]

Hello, Petrus!


Yes . . . Give us the statements!

Sorry did not notice! I fixed it now!

 

[MarkFL]

Can you begin by stating the definitions of the various plane figures given?

 

[HallsofIvy]

For example, with reference to (a), is it true that all diamonds and all rectangles are parallelograms? Or are the any parallelograms that are NOT diamond or rectangles? To answer that, obviously, you need to know the definitions of "diamond", "rectangle", and "parallelograms".

 

[Nehushtan]

Re: Plane figures

By “diamonds” you mean rhombuses, right?

 

[Petrus]

Can you begin by stating the definitions of the various plane figures given?

Rombppisite side parallel and its quadrilateral.
Rectangle: its quadrilateral and its 90 degree on corner.
Paralellograms: is a romb,square and rectangle. Quadrilateral
Trapezoid: quadraliteral, paralellograms,rectangle, romb, square ( its a isoceles trapezoid)
square: quadraliteral , same lengt all side, 90 degree, specialfall romb rectangle paralellograms,trapezoid

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By “diamonds” you mean rhombuses, right?

Yes

 

[Petrus]

Can someone try explain for me what i am doing wrong, i get (a) is correct i get (b) is false cause e don't got parallel sides, (c) is false cause e is none parallel sides, (D) is correct and (e) is false cause e is none parallel

 

[I like Serena]

Consider the following amounts of plane figures: A = {All squares}, B = {all diamonds}, C = {all rectangles}, D = {all parallelograms}, E = {all trapezoidal with three equal sides}, F = {all trapezoidal with at least a straight corner angle}. Examine which of the following statements are true. Reply with the letter R (true) or F (false).
__________ (a) B U C= D
__________ (b) D ∩ F= C
__________ (c) D ∩ E= B
_________ (d) F "subset" D U E
__________ (e) E ∩ F= B ∩ C

Any advice?

Can someone try explain for me what i am doing wrong, i get (a) is correct i get (b) is false cause e don't got parallel sides, (c) is false cause e is none parallel sides, (D) is correct and (e) is false cause e is none parallel

Hi Petrus! :)

Let's see, your sets look visually like:

A
\begin{tikzpicture}
\draw (0,0) rectangle (1,1);
\end{tikzpicture}

B
\begin{tikzpicture}
\draw (0,0)-- (1,0) -- (1.707,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}

C
\begin{tikzpicture}
\draw (0,0) rectangle (3,1);
\end{tikzpicture}

D
\begin{tikzpicture}
\draw (0,0)-- (3,0) -- (4,1) -- (1,1) -- (0,0);
\end{tikzpicture}

E
\begin{tikzpicture}
\draw (0,0)-- (2.414,0) -- (1.707,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}

F
\begin{tikzpicture}
\draw (0,0)-- (3,0) -- (3,0.707) -- (0.707,0.707) -- (0,0);
\end{tikzpicture}

Oh sorry, tikzpictures do not work yet.
(Just practicing, just in case they will work someday. ;))

View attachment 696

Let's start with (a) B U C= D.
So those are the diamonds (B) together with the rectangles (C).
And the question is whether that matches with the parallelograms (D).

Well, a diamond is a parallelogram, so that's okay.
A rectangle is a parellelogram, so that's okay too.
But... a generic parallelogram is neither a diamond nor a rectangle.

So no, (a) is not correct. It is false.

 

[Nehushtan]

Re: Plane figures

By “diamonds” you mean rhombuses, right?

Yes

Okay. I just wanted to be sure that you were not referring to kites. (A kite is a convex quadrilateral whose diagonals intersect at right angles.) (Smile)