## Saturday, August 14, 2010

### Question 2,

Dear Mr Ng,

Question 2:

Reasons: Statement A: Squares and parallelograms have 4 sides each. Proof:
Mentor:
Student:
Four.

Statement B: Opposite sides of a square and parallelogram are parallel. Proof:
Student:
But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off?
Mentor:
Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel.

Statement C: A trapezoid has only one pair of parallel sides. Proof:
The shape of a trapezium shows only one pair of parallel sides.

Question 4

Reasons: A parallelogram has 2 pairs of parallel lines, but the pairs of lines have different lengths (Let's say AB//CD and BC//AD. AB and CD have the same length (xcm) and BC and AD also have the same length but this time not xcm (example ycm)). Futhermore, all of the angles in a square are 90º. But in a parallelogram, opposite angles are the same.

Question 5

A parallelogram has 2 parallel pair of lines (BF//ED and BE//ED). Thus BFED is a parallelogram.

### Q1,2,5-Matthew Wong

Q1. The statement is justified as a square can be a rhombus as it sides are all equal. but a rhombus cannot be a square as the angle of each side might not be 90º.

Q2. (D)
A) They are quadrilaterals as they both have four sides.
B) They are parallel
C) One of the sides are parallel

Q5. Lines BF and ED are parallel and so are lines BE and FD.

### Questions 1, 2 and 4 by Tshin Qi Ren

Q1) 'A square is a rhombus but a rhombus is not a square'.
I agree with the statement.

Because a square is a polygon with four equal length sides and four 90 degree angles.
while a Rhombus is a shape that all the sides are equal with the same length but might not have the same degree, only the opposite side is the same. But a square can in a way, have the same degree for opposite sides. But a rhombus might not necessarily have 90 degrees so it cannot be said to be a square...

Q2) Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

D) All of the above.
A) Quadrilateral is a four-sided figure which have straight lines so squares and parallelograms.
B) Having the same degree for the 4 sides, the square's opposite sides are naturally the same. As their opposite degree are the same, so, the opposite sides are naturally opposite sides too.
C) A trapezoid only have 1 pair of parallel sides

Q4) 'All parallelograms are squares?' Do you agree with this statement?
No, I do not agree with it. Parallelograms are opposite sides that are parallel to each other and opposite sides are equal in length. However, their angles do not necessarily have to be 90 degrees like the square.

Tshin Qi Ren

## Friday, August 13, 2010

### E-Learning 2010 Maths Activity 3

Question 1:

The statement 'A square is a rhombus but a rhombus is not a square' is completely untrue.

First, let us review the properties of a square:

• Perpendicular lines (90 degrees in each angle)
• Parallel Lines
• All lines are equal in length

Then, compare with the properties of a rhombus:

• Parallel Lines
• All lines equal in length
• Non-perpendicular lines

Hence, since one property is completely opposing each other, rhombuses cannot be squares, and squares cannot be rhombuses.

Question 2:

All of the above! (D)

For A, a quadrilateral is a shape with 4 sides, hence, a square and a parallelogram are quadrilaterals.
For B, the opposing sides of squares and parallelograms are parallel to each other.
For C, the trapezoid has only one pair of parallel lines, no more, as the other two lines will soon connect if extended.

Question 4:

Parallelograms already have 2 different lengths for their sides, hence is not a square.

### Q2,3&4 by Chan Jia Ler

Q2: D) All of the above.
A) is correct because squares and parallelograms are all four sided, which make them quadrilaterals.
B) is correct because both opposite sides of squares and parallelograms are parallel.
C) is correct because the two sides that are sandwiching the non-parallel sides are parallel.

Q3: The figure is a trapezium, because the parallel sides of a trapezium are of the same length, and the pair of opposite angle both add up to 180º.

Q4: I do not agree with the statement, because parallelograms' two opposite sides are of the same length, but ALL sides cannot be of the same length.

### Question 1 by Kimberly Ong

A square is a rhombus as it has got 4 sides of the equal length and its opposite sides are parallel. A rhombus also has these properties. However, a rhombus does not necessary have 4 equal angles, which is a property of a square.

### Question 2 by Kimberly Ong

A) Both of them are quadrilaterals as they both have 4 sides.
B) Opposite sides of a square and a parallelogram are parallel as parallel lines do not meet.
C) A trapezoid does only have one pair of parallel sides.
D) Statement D is correct as all of the above of correct.

### Question 3 by Kimberly Ong

This quadrilateral is a trapezium. It is because it has the same properties as a trapezium will have. It has one pair of opposite sides which equal in length, the other pair not equal in length. It could not be a square or a rectangle as it does not have 4 right angles. It could not be a rhombus since it does not have 4 equal sides. It could not be a parallelogram as it does not have two pairs of parallel lines. It does not have two pairs of adjacent sides that have equal length, thus it could not be a kite.

### I do not have permission to add a sticky post on wallwisher.

Mr Ng, I do not have permission to add a sticky to Wallwisher. Why?

### Question 4 by Serene

Question 4:

'All parallelograms are squares?' Do you agree with this statement?

Ans: No, I do not agree with this statement. The property of parallelograms are that opposite sides are parallel to each other and opposite sides are equal in length. However, their angles do not necessarily have to be 90 degrees like the square.

### Question 1

Q1) Based on the above conversation discuss, with examples and justification whether the following statement is justified.

'A square is a rhombus but a rhombus is not a square'.

Ans: True, a rhombus has equal sides and so does a square. However, a rhombus' diagonally opposite angles are not 90 degrees like the square. So a square can be a rhombus as is has 4 equal sides but a rhombus cannot be considered a square as it's angles are not necessarily 90 degrees.

### Question 2

Q2) Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

Ans: D) All of the above.

A) Yes, a square and a parallelogram are quadrilaterals. A quadrilateral is a four-sided figure which have straight lines like a square and parallelogram.

B) Yes, they are. A angles of a square are all 90degrees so the opposite sides are parallel to each other. A parallelogram sides are parallel to each other as their diagonally opposite angels are equal.

C) Yes, a trapezoid has one pair of parallel sides.

### Question 3 by Ho Jun Hui

The figure is an trapezoid. First, it only has one set of parallel lines, which squares, parallelograms or rhombuses, etc have. Next is its difference in length of another set of lines. This fits the description of the parallelogram.

### Question 2 By Ho Jun Hui

A) Yes, as they all have four sides
B) Yes, if not they would not be squares or parallelograms
C) Trapezoid has one pair of parallel lines, which makes it different from a parallelogram
D) Yes, all the reasons stated above.

### Question 4 by low wei kang

question 4
No, I do not a agree with this statement as the sides of the squares are all equal, while some of the sides of the parallelogram are not equal, also, the angles of the square are all similar, but some the angles of the parallelogram are not equal.

### question 5 by low wei kang

Question 5
I agree with this statement, as the sides of the parallelogram has similar sides, the half of one of its side would be equal to the half of the other, and as they are half the sides 2 the opposite sides, they should also be on opposite sides, which are parallel.

### Question 1 by low wei kang

Weikang
Question one
'A square is a rhombus but a rhombus is not a square'.
I agree with this statement as the rhombus needs to have equal sides and opposite angles to be similar, in which the square has all the needed things to be a rhombus, but the square requires all the angles to have a similar angle, which is something the rhombus does not have, therefore the square can be a rhombus but the rhombus cannot be a square

### Question 4 by Roy Chua

I disagree with the statement, for not all parallelograms have sides that are all equal, which is the situation in that of a square. Not all parallelogram's angles are all equal to one another, which is the situation in that of a square.

### Question 4 Millie Thng

'All parallelograms are squares?' Do you agree with this statement? Justify your answer with example/s.

I do not agree with this statement. Attached is a parallelogram that is not a square. It has 2 pairs of parallel lines and 4 sides (thus a parallelogram) but all 4 angles are not at 90 degrees each (thus it is not a square).

picture taken from : http://sodilinux.itd.cnr.it/sdl6x3/documentazione/xeukleides/eukleides_html/samples/parallelogram.html

### Question 2 Millie Thng

Which of the given statements is correct? Justify your answer/s with examples.
A ) A square and a parallelogram are quadrilaterals.
B ) Opposite sides of a square and a parallelogram are parallel.
C ) A trapezoid has one pair of parallel sides.
D ) All the above

D is correct.
A) A square and a parallelogram have four sides each so they are quadrilaterals.
B) The opposite sides of a square and a parallelogram will never meet when extended.
C) There is only one pair of sides in a trapezoid that will never meet when extended.

### Question 2 by Roy Chua

Statement D is correct for:
A) Both squares and parallelograms have four sides altogether, meaning they are quadrilaterals.
B) Squares and parallelograms have parallel opposite sides for when any one of the angles within both shapes are added with one of the angles adjacent to it, the result is 180 degrees.
C) This is true for if they had two pairs and still are quadrilaterals, they would be squares or rectangles. If they had no pairs of parallel sides, the shape would not be a trapezium anymore.

### Question 1 Millie Thng

Q1 Based on the above conversation discuss, with examples and justification whether the following statement is justified. 'A square is a rhombus but a rhombus is not a square'.

The statement is true. A square is a rhombus because it fulfills the criteria - having all four sides with the same length, 2 pairs of parallel lines. A rhombus is not a square because it does not fulfill the criteria of being a square - it does not have all 4 angles at 90 degrees each.

I do not agree that all parallelograms are squares. The sides of a parallelogram are of unequal lengths, while the sides of a square are equal. The sides of a parallelogram are not perpendicular to one another, while the sides of a square are perpendicular to one another. Parallelograms can also exist in forms of a rectangles or rhombuses

### Question 2 by Mitchel Goh

Statement D is correct. A square and a parallelogram are quadrilaterals as they have 4 sides. Opposite sides of a square and a parallelogram are parallel, since parallel lines do not meet. A trapezoid has only one pair of parallel lines-the top base and the bottom base are parallel to each other. All the statements are correct, thus the answer is D.

### Question 1 by Mitchel Goh

`I agree with the statement.Every square is a rhombus, because it's a quadrilateral with four congruent (equal) sides.  But there are rhombuses that are not square,because their angles are not right angles. `

### Question 1 by Roy Chua

The statement is true for all the opposite angles of a square are the same and all the opposite sides of a square are of the same length. A rhombus is not a square for not all rhombi's angles are the same and are right-angles, and not all the sides of all rhombi are perpendicular to sides adjacent to itself.

### Question 4 by Denise Lim

I do not agree that all parallelograms are squares. The sides of a parallelogram are of unequal lengths, while the sides of a square are equal. The sides of a parallelogram are not perpendicular to one another, while the sides of a square are perpendicular to one another.

### Question 2 by Denise Lim

Statement D is correct. A square and a parallelogram are quadrilaterals as they have 4 sides. Opposite sides of a square and a parallelogram are parallel, since parallel lines do not meet. A trapezoid has only one pair of parallel lines-the top base and the bottom base are parallel to each other. All the statements are correct, therefore the answer is statement D.

### Question 1 by Denise Lim

The statement is true. A square is a rhombus as all the sides of a square are equal and they are parallel to one another. However, a rhombus is not a square since a square has 4 right angles and most rhombus do not.

### Question 4 by Arthur Lee

I do not agree with the statement as there are major differences between a parallelogram and a square. The sides are not equal in length in the parallelogram while this is so on the square. The angles are not all 90 degrees in parallelogram while in a square all angles are 90 degrees.

### Question 2 by Arthur Lee

Question 2:

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

Answer: D) A is correct as according to the shapes they both have four sides. B is correct as according to the shapes the opposite sides are parallel. C is correct as only the bottom side is parallel to the top. Thus, the answer is D.

### Question 1 by Arthur Lee

The statement is not justified as a square is not a rhombus or vice versa, they are two completely things. Although all sides have equal length is evident in both, their angles are not the same and the overall structure is completely different.

### Question 4 by Fatin Zafirah

A parallelogram does not have four right angles like a square. A parallelogram also does not have 4 equal sides like a square.

### Question 2 by Fatin Zafirah

D) All of the above

Quadrilaterals have four sides. Both the square and parallelogram have four sides.

The lines on the opposite sides of the square and parallelogram will never meet. Therefore they are parallel.

Only one pair of lines of the opposites sides of the trapezoid will never meet. Therefore it has only one pair of parallel sides.

### Question 1 by Fatin Zafirah

A square is a rhombus but a rhombus is not a square. Both the square and rhombus are parallel. However, the rhombus does not have four right angles so it is not a square.

### Question 5 Done By Ilya Haider

BFDE is a parallelogram as the 2 equilateral triangles, ABE and CDF are at the sides of ABCD. This leaves the space in the middle. This space BFDE is a parallelogram.

### Question 4 Done By Ilya Haider

All parallelograms are not squares as there is a shape called the rhombus of which all horizontal and vertical sides are parallel to each other.

### Question 3 Done By Ilya Haider

This figure is a trapezoid. It only has 2 sides of equal length. The total angle inside any figure is 360 Degrees. So, one side of the figure has 2 angles which add up to 180 Degrees. Same for the other 2 angles.

### Question 2 by Jeremy Lai

I agree with all of the statements. A square and a parallelogram are
quadrilaterals as they are four sided figures. Opposite sides of a
square and a parallelogram are parallel. A trapezoid has one pair of
parallel lines.

### Question 4 by Jeremy Lai

I disagree with the statement "all parallelograms are squares".
Parallelograms are not squares as it does not have any perpendicular
lines, and does not have four right angles.

### Question 1 by Jeremy Lai

A square is a rhombus as it has four equal sides and its sides are
all parallel. However, a rhombus is not a square as a rhombus does not
always have four right angles.

### Question 2 Done By Ilya Haider

My answer is D) All of the above. For A) A square and a parallelogram are both quadrilaterals because both of them have 4 sides. B) Opposite sides of a square and a parallelogram are parallel. C) A trapezoid has only one pair of parallel lines.

### Question 1 Done By Ilya Haider

A square is a rhombus as for both shapes, they have 4 sides which are parallel to each other and are of equal length. A rhombus is similar to a square but not a square. It's sides are slanted at a certain angle. A square is a rhombus but a rhombus is not a square.

### Q4 by helene tan

'All parallelograms are squares.' I disagree with this statement as parallelograms are not squares. Their interior angles are not 90 degrees, so they are not squares. Parallelograms also do not have 4 equal sides, like a square does.

### Question 1

A square is a rhombus as for both shapes, they have 4 sides which are parallel to each other and are of equal length. A rhombus is similar to a square but not a square. It's sides are slanted at a certain angle. A square is a rhombus but a rhombus is not a square.

### Q2 by Helene Tan

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

A is correct as both the square and the parallelogram are four-sided figures. B is correct as the opposite sides of a square and parallelogram will never meet if it is stretched to be longer. C is correct as only one pair of lines of a trapezoid will not meet if it is stretched, so it has only one pair of parallel sides. Therefore, the answer D, all of the above, is correct.

### Q1 by Helene Tan

'A square is a rhombus but a rhombus is not a square'. This statement is untrue, as a square is not a rhombus, and a rhombus is not a square as well. Although both have two sets of parallel lines, and both have 4 equal sides, a square has a 90 degree angle whereas the rhombus does not.

### Question 1 Activity 3

This statement is untrue as neither square nor rhombus are the same. A rhombus and square may have parallel sides but a square had a 90 degree angle but a rhombus does not. So, this statement is untrue.

### Question 5 by Reuven Lim

BFDE must be a parallelogram. This is because BC and AD are opposite sides and parallel. As E is the midpoint of AD, and F the midpoint of BC, BE and FD are parallel. BF and ED are also parallel, so BFDE must be a parallelogram.

### Question 4 by Reuven Lim

I do not agree with this statement. Not all parallelograms are squares. Parallelograms are not even squares. All sides of squares are equal, and all interior angles = 90 degrees each. All sides of parallelograms are not equal, and all interior angles not = 90 degrees each. Therefore, the statement is false.

### Question 3 by Reuven Lim

This figure should be a trapezoid. This is because only one pair of opposite sides are equal in length, and the other pair is of different lengths. This leaves only the trapezoid left, so the figure should be a trapezoid.

### Question 2 by Reuven Lim

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

Yes, because they have four sides so they qualify.

B ) Opposite sides of a square and a parallelogram are parallel.

Yes.

C ) A trapezoid has one pair of parallel sides.

Yes.

D ) All the above

Yes.

### Question 1 by Reuven Lim

The statement is not justified. A square is not a rhombus and a rhombus is not a square. This is because in squares, all interior angles = 90 degrees each. In a rhombus, all the interior angles are not = 90 degrees each. Therefore, a square is not a rhombus and a rhombus is not a square.