## Sunday, August 15, 2010

### Questions 2, 3 and 4 by Goh Chin Fan

Question 2:
Option D is correct.
A square and a parallelogram are quadrilaterals as they are both 4-sided.
Opposite sides of a square and a parallelogram are parallel:

Question 3:
The quadrilateral is a trapezium. A trapezium has one pair of opposite sides equal in length, which is the pair of lines that are not parallel to each other, and the other pair not equal in length, which is the pair of lines that are parallel to each other. It also has a pair of opposite angles that are supplementary.

Question 4:
No, I do not agree with the statement. The lines of a parallelogram are not of equal length, only the opposing lines are of the same length, while for the square, all lines are of equal length. Therefore I do not agree that all parallelograms are of equal length.

## Saturday, August 14, 2010

### Question 1 by Elgin Low (the post below not named is also mine, please see the comment inside to determine question)

A rhombus is just a quadrilateral with equal length. It does not mean that the angles of the 4 sides have to be the same. However, a rhombus is not a square as that means that all rhombuses are squares. Squares are quadrilaterals with 90 degrees on each of its four sides. Rhombuses have different angles that do not for 90 degrees. They however, can have any random angle as long as all the angles equal to 360 degrees. A square can be a rhombus as its angles equal to 360 degrees, and its sides are of equal length.

My answer: all of the above are correct.

1. A quadrilateral is a figure with 4 sides. Both a parallelogram and a square have 4 sides exactly.
2. Opposite sides of a square and parallelogram are equal. This is proved on a square as all the sides are 90 degrees. For a parallelogram, proof that its sides are parallel, is that each pair of sides are all of equal length.
3. A trapezoid does have only 1 pair of parallel lines. It is a figure that has one pair of parallel lines of equal length, and 2 other sides with unequal length.

### Question 4 by Elgin Low

Parallelograms are not squares. A square's sides are all equal while a parallelogram is not. Here is proof of it. As you can see, a pair of the sides of a parallelogram is 1.22m, while the other is 2m. This is not a square.

## Friday, August 13, 2010

### Question 1 - 5 by Marcus

Q 1 : I agree with the statement because a square may be a rhombus because, it has four equal sides, two pairs of parallel lines while a rhombus may not be a square because a square has 4 perpendicular corners which a rhombus does not have.
Q 2 : Options A, B, C and D are all correct. A is correct      (as you can see in the picture)
Q 3 : The figure is a trapezium. The two sides that are equal are the sides that are not parallel to each other, the sides that are parallel to each other is the sides that are not of equal length and in this way, the opposite angles will sum up to 180.

Q4 : Not all parallelograms are squares. Evidence : this definitely does not have four equal sides

Q5 : BFDE is a parallelogram because line BC and AD are equal, so when you draw a new line from B to E and D to F, those two are same in length and is parallel

### Q2 (Continued)

Sorry for the double post. I only realised that I missed out a section of Q2 after I sent the email.

*Continued*

Q2
All of the statements are correct. Squares and Parallelograms are quadrilaterals as they both have 4 sides each. Opposite sides of Squares and a Parallelograms are parallel as the two lines never meet even if they go on forever. A Trapezoid only has one pair of parallel sides as the of the other pair  of sides if extended, will eventually meet each other. Meaning that a Trapezoid only has one pair of parallel sides.

### eLearning Maths Activity 3 (Sean Phua Aik Han) Q1, Q2, Q4

Q1
A Square is a Rhombus as a Square has all the properties that a Rhombus has, two pairs of equal sides that are parallel to each other and that all sides are of equal length . However, all the angles in a Square are right angles (90 degrees). While in a Rhombus, the angles in it are not right angles (90 degrees). Thus, it can be said that a Square is a Rhombus but a Rhombus is not a Square.

Q2
All of the statements are correct. Squares and Parallelograms are quadrilaterals as they both have 4 sides each. Opposite sides of Squares and a Parallelograms are parallel as the two lines never meet even if they go on forever.

Q4
No, I do not agree with this statement. Parallelograms do not have 4 equal sides, which is a property of a square. This alone makes it impossible for all Parallelograms to be a square. Unless it is a Parallelogram which has 4 equal sides, in which the shape would be called a Rhombus instead of a Parallelogram.

### Q1, Q2, Q4(Shawn Lim)

Question 1
A square is a rhombus because it fills all the properties of a rhombus. The square has two pairs of opposite sides that are parallel and all its sides are of equal length. A conventional rhombus is not a square because the angles of a rhombus are not right angles.

Question 2
I think that the statement D is correct. A square and a parallelogram both are four sided figures so they are quadrilaterals. The opposite angles of a square and parallelogram are equal so the opposite sides are parallelogram and a trapezoid indeed has a pair of parallel sides.

Question 4
Not all parallelograms are squares because not all sides of a parallelogram are equal and one of the properties of a square is that all the sides have to be equal.

### Question 2, 3 and 4 (Elgin Patt)

Q2. (All of the above)Quadriletral means 4 sided. So both a Square and Parallelogram have 4 sides.
Both the square and parallelogram have opposite sides that are equal.
A trapezoid has 4 lines, and only 1 pair is parallel.

Q3. It is a trapezium. If you add up the 2 opposite sides of a Trapezium, it would be equal to 180 degrees. Its top and bottom lines are also parallel to each other.

Q4. I do not agree with the statement. Parallelograms can have different lengths and can still be called a parallelogram. Whereas in the case of squares, they need to have equal lengths for all sides.

### chuazongwei q1,2,4

question 1:
i think that the statement is justified, as a square has a equal length for each of its sides, and qualifies the requirements to be a rhombus. but a rhombus might not fulfill the requirements to be a square, like the requirement that all sides of the figure must be parallel in order to be a square.

question 2:
i think that all of the answers are correct, as a trapezoid is indeed a four sided figure with only one set of parallel lines, while Squares and parallelograms are quadrilaterals as both have 4 sides each, and the opposite sides of a square and parallelogram are parallel, because as far as they go on, they will never meet.

question 4:
No. I do not agree with this statement as not all of the different types of parallelograms have equal length in each side, therefore it does not fufill the requirement to be a square

### Question 1 by Liau Zheng En

I agree with the statement.

A square is a rhombus as all of its sides are equal and the sum of supplementary angles is 180°. But the rhombus is not a square as the angle of a rhombus is not always a right angle. The angle of a rhombus may differ.

### Question 5 by Liau Zheng En

Question 5

Since the point of intersection is in the midpoint, the figure would already be divided equal, being that the side of the figure would be parallel. If a line is cut through form point E to point F, The parallelogram will form two parallelogram. The sides of the figure can then be concluded that they are parallel. Using the points noted down, it can be concluded to be a parallelogram.

### Question 4 by Liau Zheng En

Question 4

I disagree with the statement.

A parallelogram has opposite sides which are parallel, similar to a square. The sum of the angles of both shapes are the same too.
But the square has 4 equal sides, unlike the parallelogram which opposite sides are the same. The corner of a square is a right angle while the angle of the parallelogram differs.

Square

Parallelogram

### Question 5 by Dionne Choo

BFDE is a parallelogram as we know that AD is parallel to BC, so DE is definitely parallel to BF. Since BC and AD are of the same length, then BE and DF should be parallel too. Thus, BFDE is a parallelogram as it has 2 sets of parallel sides.

### Question 4 by Dionne Choo

No. I do not agree with this statement. All parallelograms do not have equal sides, and so are not considered squares.

### Question 3 by Dionne Choo

This figure is a trapezium. A trapezium has a pair of parallel sides, and one set of opposite sides are parallel but not equal. Also, there is a pair of opposite angles that are supplementary.

### Question 2 by Dionne Choo

D) All of the above

Squares and parallelograms are quadrilaterals as both have 4 sides each.

The opposite sides of a square and parallelogram are parallel, because as far as they go on, they will never meet.

A trapezoid has only one pair of parallel sides, because the other pair is not parallel.

### Question 1 by Dionne Choo

The statement ' a square is a rhombus but a rhombus is not a square' is justified. This is because the definition of a square is that all opposite sides are parallel, all sides are equal and adjacent sides are perpendicular. However, the definition of a rhombus is that all opposite sides are parallel and all sides are equal. Adjacent sides need not be parallel. So, a square is a rhombus, but a rhombus is not a square.

### Question 1, 4 & 5 by Lim Hao Yang

Question 1

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

I agree with this statement.

The square and the rhombus share similar properties. Both the square and the rhombus has 4 equal side, opposites which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equals.

However, not all rhombi are squares. A rhombus may not always have right angles.

Question 4

All parallelograms are squares.

I disagree with this statement.

The parallelogram and the square share similar properties. Both the parallelogram and the square have their opposite sides of the same length, which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equal.

However, not all parallelograms are squares as the lengths of all 4 sides may differ.

Question 5

BFDE must be a parallelogram.

According to the picture, the length of BC and AD is x. So, the length of ED and BF must be 1/2 x. Since ED and BF are of the same length as are parallel, we can conclude that BE and DF are both parallel and of the same length.

### Sun Jie Min

The earlier post was by Sun Jie Min

### Activity 3 Questions 1,2,4

Q1: The statement is true. A rhombus has four sides with the same length. The opposite sides are parallel. A square has four sides with the same length, parallel opposite sides and four right angles.

Q2: Statement D is correct. Squares and parallelograms are quadrilaterals as they are polygons with four sides. Opposite sides of a square and a parallelogram are parallel as the adjacent angles are supplementary. A trapezoid has one pair of parallel sides as it has two pairs of supplementary angles.

Q4: I do not agree with the statement. Not all parallelograms are squares. Parallelograms have two pairs of parallel sides. The opposite sides are of equal length and the opposite angles are of equal measure. A square has four sides with the same length, parallel opposite sides and four right angles. Parallelograms do not have four sides with the same length and four right angles. Thus, parallelograms do not necessarily have to be squares.

### Question four by Tam Wai Hang

BFED has 4 sides, so it is a quadrilateral.
BF//ED and BE//FD
BF=ED and BE=FD
<BFE=<EFD, making the figure a parallelogram.

### question 2 by Yeo Jun Jie

Solution to question 2:

Question 2
D) all of the above.

Squares and parallelograms have four sides, therefor they are quadrilaterals.
Squares and parallelograms have 2 sets of opposite sides.
A trapezoid has only 1 pair of parallel lines.

### Question 3 by Yeo Jun Jie

Here is my solution to question 3.

### Question three by Tam Wai Hang

The figure is a trapezium.

### Question 5 by Yeo Jun Jie

Solution to question 5.

### Question two by Tam Wai Hang

Answer: D) All of the above

Reason:
1) A quadrilateral has four sides. And both the parallelogram and a square fulfills that criteria.

2) Both the parallelogram and the square have parallel lines.

3) The trapezoid only has one pair of parallel lines while the other two sides are not.

### Activity 3 by Yeo Jun Jie

Here are my solutions. I have put them together in a pdf file

### Question 5 by Tang Wen Yue

The distances between lines BF and ED are constantly the half the distance between BC and AD,which means they are parallel.
BF and ED are parallel as they are on lines BC and AD,which are parallel.
That makes BFDE a parallelogram.