summary for 22/8/10

• NEVER cross multiply when there is no equal sign in the equation.
• Always do the inner most bracket first.
• All x intercept are called Roots.
• The y intercept of the curve line/parabola is the product of the y intercepts of the original straight lines.
• The x intercept of the curve is the same as the original straight lines.

Summary for 24/8/10

Tuesday's math lesson summary by Celine

Finding the equation of a line.

First deduce the gradient through the formula Rise over Run. Then substitute the the co-ordinates of the first point to deduce the y-intercept.

To get a faster equation: Change the equation into the format (x/a + y/b = 1)

Ex. y = 1/2x - 3

1/2x + y = -3

x/-2 + y/1 = -3

x/6 + y/-3 = 1 //

However, if the the question asks for the equation in terms of y=mx+c, just do it like this:

x/6 + y/-3 = 1

-3x/6+y = -3

-1/2x + y = -3

y = 1/2x -3//

Question: When doing x/a + y/b = 1, why must it equal to 1?

Summary for 20/8/10's lesson...

Kristin Chai(1)- 20/8/10(Friday)

Linear Graphs
For questions similar to example 07 you must REMEMBER that the final line MUST be a equation nothing else.
Also, y=mx+c. In order to find C we need to know y.Therefore,there will only have 1 unknown.
We can substitute some of the coordinates and we can find out what is C.

Finding the Gradient:
We need to change the equation into y=mx+c.
When the questions say it is parallel that means the gradient is the same.
Also,if the line is horizontal the gradient will be 0.

SUMMARY OF LINEAR EQUATIONS ...

ANONYMOUS - 17th August 2010

1. Today we reconsidered the linear equation & the general form of a linear equation is y = mx + c
2. where by the m refers to the GRADIENT
3. where c is the Y-INTERCEPT (or the value of y when x = 0)
4. m is POSITIVE when as x increases, y also increases
5. m is NEGATIVE when as x increases, y will decrease
6. m is ZERO when as x changes, y is constant (HORIZONTAL LINE)
7. m is undefined when x is constant and y changes (VERTICAL LINE)
8. X-INTERCEPT would be equal to -c / m ... (or the value of x when y = 0)

NOTE - c (or the constant in all the equation) is always the y-intercept, even for equations such as y = ax^2 + bx + c ...

Why do you think this is so? (HINT - look at point (3) above)

Prove point (8) for yourself ...

Question 2,

•Q2.

(D) All of the above.

-(a) Quadrilaterals refer to figures with four sides. Both a square and a parallelogram have four sides, thus both are quadrilaterals.

-(b) There are lines in a square and a parallelogram that are side by side and having the same distance continuously between them, thus they are parallel.

-(c) A trapezoid has two line parallel to each other, which is the bottom line and the top line.

•Q4.

No, I do not agree with this statement.

A parallelogram is a figure with 2 pairs of parallel lines.

In a rhombus/rectangle, this rule applies too as in both figures, there are 2 pairs of parallel lines.

This the statement is wrong.

•Q5.

BF and ED are both halves of BC and AD respectively. Since BC and AD are equal in length, BF and ED are equal as E and F is the midpoint of BC and AD. When BF and ED are equal, BE and FD must also be equal since both are parallel to each other.

:D

Activity 3 elearning (ong bing jue)

Quadrilaterals have four sides,four angles and the interior angles of each sides added together make up 360 degrees

2a.Quadrilaterals have four sides,four angles and the interior angles of each sides added together make up 360 degrees.A square and a parallelogram both have four sides and angles and these angles make up 360 degrees when added together.Thus a square and parallelogram are quadrilaterals.

2b.Yes.Angles of the opposite sides added together should make 180 degrees which shows they are parallel and never cuts each other.

2c.A trapezoid has only one sides of parallel lines because it has only 2 pairs of opposite angles makes 180 degrees when added together while figures with 4 pairs of opposite angles which makes up 180 degrees when added together has 2 pairs of parallel lines.

Thus All of the above are correct.

3.Only a trapezium which is a quadrilateral has only one parallel lines.

4.No.They make up a rectangle.A parallelogram is made up of a square and 2 triangles.

 Let's give an example:(Image Above)

A parallelogram which has a base of 8 cm and height of 3 cm.Let's cut the parallelogram into 3 parts.A rectangle,and 2 triangles,let's combine the 2 triangles and make a square.When you combine the rectangle and the combined rectangle of the two triangles you from a new rectangle of 8 x 3cm. 8 x 3cm is 24 cm square which is not a square number.

5.Since ABCD is a parallelogram and E and F is the midpoints. Since AD = BC and AE=ED  which means (AE=ED) is equals to BF =FC thus AE = ED = BF = ED. As angle EBF = AEB

So angle BED + EBF =180 degrees and EDF = EBF.Thus it is a parallelogram.

Maths Activity 3 (Qn 3, 4 and 5)

Q3.

The figure is a trapezoid as it satisfy all the requirement.

Q4.

not all parallelograms are squares as squares have four right angles everytime but parallelogram does not have four right angles all the time.

Q5.

BF and ED is the same as E and F is the midpoint, also, BC and AD are of the same length. when BF and ED are equal, BE and Fd must also be equal as they are now parallel to each other.

Done By JingHeng

(pls ignore the same post below as there is no name)

MAths Activity 3 (Qn 3, 4, 5)

Q3.

The figure is a trapezoid as it satisfy all the requirement.

Q4.

not all parallelograms are squares as squares have four right angles everytime but parallelogram does not have four right angles all the time.

Q5.

BF and ED is the same as E and F is the midpoint, also, BC and AD are of the same length. when BF and ED are equal, BE and Fd must also be equal as they are now parallel to each other.

Math activity 3 (Q1,Q3 and Q4)

Question 1:

A square is a quadrilateral where all 4 sides are equal, opposite sides are parallel and every meeting point of 2 lines are 90 degrees.

A rhombus is a quadrilateral where all 4 sides are equal, opposite sides are parallel and meeting points of 2 lines can be of any degree.

So a square is a rhombus as all 4 sides are equal and opposite sides are parallel while a rhombus is not a square as a Rhombus might not have 90 degrees.

Question 3:

It would be a trapezium, 

a trapezium would have a 1 pair of opposite line with different length and the other of the same length while diagonally opposite angles would add up to 180 degrees.

Question 4:

No, all squares have right angles while only some parallelogram have right angles.

 

Maths e-Learning Activity 3 =>

Question 1:     
A conversation between a mentor and a student. 
Mentor:     Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?
Student:    Yes. Lines like that are called parallel lines.
Mentor:     Great! We've already learned that quadrilaterals have how many sides? 
Student:    Four.
Mentor:     That's right and we call quadrilaterals with parallel sides parallelograms.
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, like this:

Student:     Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!

Mentor:      Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.
Student:     So a rhombus is a type of parallelogram just like a banana is a type of fruit.
Mentor:      Right, we should not say that all parallelograms are rhombus, just like we don't say that all fruits are bananas.

Ans:

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

Is this true? A rhombus is a special type of square, but a square is not a rhombus.

Why is that so? A square has 4 sides and 2 lines side by side will meet at the angle of 90 degrees. While the rhombus lines side by side will meet at any angle. 

Just to add on. Lines at the sides are parallel at both rhombus and square

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

Ans:

All of the above

Question 3:

A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary¹. Identify this figure, and justify your answer with reasons.

Ans:

It is a trapezium. A trapezium has pair of parallel lines, however, the other pair is not equal and parallel, thus it would look something like this:

_____________________________________________________

\                                                                                                        /

 \                                                                                                     /

  \                                                                                                  /

   \                                                                                               /

    \                                                                                             /

Question 4:

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

Ans:

Yes, all four sides of the squares are

parallelogram

Question 5:

ABCD is a parallelogram. If E is midpoint of AD and  F is midpoint of BC show, with reasons, that BFDE must be a parallelogram.

The key property of a parallelogram has four sides, each line directly opposite is parellel. BFDE has this key property, thus, it is a parallelogram.

--      

Aaron Sng S1-08 (18)

Question 2,3 and 4 by Ethan Soh

Question 2

My answer is D. Both the square and parallelogram are quadrilaterals because they both have four sides. Both the sides of the square and parallelogram's are parallel because they are facing each other. The trapezoid only has one pair of parallel sides, which is its top and bottom.

Question 3

The angles on a straight line add up to 180. The angles on parallel lines also add up to 180. This figure is a parallelogram.

Question 4

No, I do not agree with this statement. This is because squares have all four equal-length sides, whereas parallelograms do not have four equal-length sides.

Maths Activity 3. Ng Kok Yin. Question: 1,3,4.

Question 1:

A rhombus has to have four sides that are parallel to each other. The sides must also be of the same length.

A square has to have four sides that are parallel to each other and are of same length. The angles of all four corners must be 90 degrees.

Hence, a square is a rhombus as a square has four sides and all parallel to each other and the sides are of the same length but a rhombus is not a square as the rhombus's four corners are not 90 degrees.

Question 3:

The figure is a Parallelogram.

It is a parallelogram as the opposite sides is equal in length while the other pair is not. 

Example:

One pair is 7.2cm while the other is 5.29.

The opposite angles are supplementary.

Example:

120.45 degree + 59.55 degree = 180 degree.

Question 4:

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

Justify your answer with example/s.

I disagree. For example, all females are humans but not all humans are females. For a parallelogram to be a square,it has to have four sides that are parallel to each other and are of same length and the angles of all four corners must be 90 degrees. 

Question 2,3 and 4 By Soe Yan Naung@Norman

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

Ans: (D). A square and parallelogram both have four sides so they both are quadrilaterals. Both the square and parallelogram has four sides and the opposite sides are parallel to each other which is their property. A trapezoid is a quadrilateral with only two sides parallel to each other like a trapezium.

Question 3: A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary1. Identify this figure, and justify your answer with reasons.

This quadrilateral can be a trapezium which only has one pair of parallel line and two of its sides are of the same length while two are of different lengths. The angles lying on different parallel lines of a side of a trapezium also adds up to 180^0. 

Question 4: 'All parallelograms are squares?' Do you agree with this statement? Justify your answer with example/s.

I do not agree with this statement. A square must have four equal sides but a parallelogram does not need all its sides to be of equal length and a square must have interior angles of 90⁰ only where a parallelogram does not need to be. So, all parallelograms are not squares.

Math E-Learning (Eunice)

Question 1:    



Read through the conversation between a mentor and a student.


Mentor:         Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?

Student:        Yes. Lines like that are called parallel lines.

Mentor:         Great! We've already learned that quadrilaterals have how many sides?

Student:        Four.

Mentor:         That's right and we call quadrilaterals with parallel sides parallelograms.

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, like this:


(picture)

Student:        Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!
Mentor:         Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.

Student:        So a rhombus is a type of parallelogram just like a banana is a type of fruit.

Mentor:         Right, we should not say that all parallelograms are rhombi, just like we don't say that all fruits are bananas.
  
Question for discussion
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'

 
Answer:    This statement is true, as the definition of a rhombus is that opposite sides are parallel to each other, and a square fulfills this definition. However, a square must not only have its opposite sides parallel to each other, the corners must be at a right angle, which means that the not all rhombuses can be a square.

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

Question 3:

A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary1. Identify this figure, and justify your answer with reasons.

Answer:    This quadrilateral is a trapezium, as definition of a trapezium has at least one set of parallel lines, without stating whether the length of the lines have to be equal, or if the other two lines are parallel to each other or must be of a certain length.


**1 sum of two angles equals 1800
 

Question 4:

'All parallelograms are squares?' Do you agree with this statement?
Justify your answer with example/s.
 
Answer:    No, not all parallelograms are squares. Square must have its corners at a right angle, but not all parallelograms fulfill this condition.

Question 5:



ABCD is a parallelogram. If E is midpoint of AD and  F is midpoint of BC show, with reasons, that BFDE must be a parallelogram.
 
Answer:    BF has the same length as ED, and they are parallel to each other, which means that BE and FD are also of the same length and are parallel to each other. When both sets of lines are parallel and have the same length as each other, it will be called a parallelogram.

Question 2,3,4 by Celine Chee

Q2. D. Squares and parallelograms are quadrilaterals as they have four sides each. In squares, all four sides are equal, so they are parallel. In parallelograms, they have two pairs of equal sides, and therefore, two pairs of parallel sides. And also, trapezoids are trapeziums, who have one pair of equal and parallel sides.

Q3. It is a parallelogram. Parallelograms have two pairs of parallel and equal sides, which one pair does not have to be equal to the other. Also, because it has two parallel pairs, its opposite angles will equal to 180 degrees.

Q4. No, I do not agree with this statement. In a square, all four sides are equal, but in a parallelogram, its four sides are not equal to each other. Also in a square, all its interior angles are 90 degrees, whereas in a parallelogram, its interior angles do not equal to 90 degrees always.

Question 2,4 & 5 by Yeo Jun Peng

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

Ans : D

Explanation:

Quadrilaterals are a four-sided figure. Both the square and the parallelogram are four-sided figure, hence they are quadrilateral.

Then length of each side of the square are same, hence opposite sides of a square are parallel. The length of opposite side of the parallelogram are parallel to each other. Hence both the square and parallelogram have opposite sides that are parallel.

Question 4:

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

Ans: No I do not agree with this statement. A parallelogram is a quadrilateral with two pairs of parallel sides. Even though the square is like that, there are also other shapes that fulfill these points. A few examples are rhombus, trapezium and rectangle.

Question 5:

ABCD is a parallelogram. If E is midpoint of AD and F is midpoint of BC show, with reasons, that BFDE must be a parallelogram.

Ans: The opposite sides are the same and parallel to each other. The adjacent angles adds up to 180 degrees and the opposite angles are the same.Therefore, we can conclude that it is a parallelogram.

Question 1, 4 , 5 by Kang Yan

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'.

A rhombus has 2 pairs of parallel lines and the length of all the sides are equal. A square has 2 pairs of parallel lines, the length of all the sides are equal and has 4 right angles. Since the properties of the square fall under the properties of the rhombus, the square is considered a special type of rhombus.

    

Source: http://www.analyzemath.com/Geometry/rhombus_problems.html

             http://mathforum.org/trscavo/tangrams/area-answers.html

Q4.

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

Justify your answer with example/s.

No, I do not agree with this statement. Just like all surgeons are doctors but not all doctors are surgeons, all squares are parallelograms but not all parallelograms are squares. In order for a parallelogram to be a square as well, it must have 2 pairs of parallel sides, 4 right angles and 4 sides of equal lengths.

                  

Source: http://www.geometry-help.info/Area_of_a_Parallelogram.html

             http://mathforum.org/trscavo/tangrams/area-answers.html

Q5.

ABCD is a parallelogram. If E is midpoint of AD and  F is midpoint of BC show, with reasons, that BFDE must be a parallelogram.

If BFDE must be a parallelogram, its opposite sides must be of equal length and are parallel to each other. Since E is the midpoint of AD and F is the midpoint of BC, the length of BE should be the same as the length of DF and BE should also be parallel to DF. BF is confirmed parallel to DE. From all these reasons, BFDE must be a parallelogram.   

Maths Activity 3 - Michelle Lim.

Q2:

D. All of the above.

Both the square and parallelogram has 4 sides and 4 straight lines.

Since the square and parallelogram has 4 straight lines, the opposite sides will be parallel.

A trapezoid has the bottom and top line parallel.

Q3)

It should be a parallelogram, as, since they are parallel, the angles opposite each other will be the same, since 360 degrees makes a whole circle, which is also the whole shape, if the sum of one opposite side is equal to 180degrees, the whole parallelogram will be 360 degrees. So, it should be a parallelogram.

Q4) 

No, i disagree with this statement. A square has parallel lines. But, the whole shape must be the same length, however, in the parallelogram, the length can differ. So, in this case, the angles of the parallelogram can be different. But, the angle of the square remains as 90 degrees.

Question 2, 3 and 4 by Wee Ren Chang

Question 2

All statements are correct. For A, a square and parallelogram are all quadrilaterals as they have four sides, as what a quadrilateral should have. For B, the opposite sides of the square and parallelogram are parallel, therefore statement B is correct. For C, a trapezoid is what we learned in primary school as a trapezium. We have been taught that trapeziums have one pair of parallel sides which are at the top and the bottom of the trapezium.

Question 3

I think this quadrilateral is a trapezium where the length of the non parallel sides are equal. This trapezium fits into the description of the quadrilateral described.

Question 4

I disagree with this statement. Although a square is a parallelogram, as they have the properties of a parallelogram, the "common" parallelogram is a quadrilateral with two pairs of sides that are parallel to each other. However, the thing that differentiates the parallelogram from the square is the parallelogram's sides are not equal in length.

Source of images: http://en.wikipedia.org/wiki/Quadrilateral

Maths Activity 3-Kristin Chai

Q2: Answer is D.
The square and parallelogram are quadrilaterals as they are 4 sided which is correct.If the opposite sides of a square and a parallelogram are not parallel,they are not even squares or parallelograms and they will be other shapes.Also,they have a pair of parallel sides if not they will not look like a square or parallelogram.

Q3:It should be a parallelogram as a pair of opposite angles that are supplementary which is 180 degree as the parallelogram have a pair of parallel lines so the angels should be 180 degrees.Even though the other pair of length is not the same,the angels will still add up yo 180 degree.Thus,it is a parallelogram.

Q4: I do not agree with the statement as you see the parallelograms are titled.Even though the lines are parallel the 4 sides of the parallelogram is not the same and also the angels are not 90 degree.So parallelograms are not squares.

E learning Maths

Attached is my work

Eugene Liow

Math activity 3 (Q2, 3, 4)

Q2 Ans : D

     Quadrilaterals are a four-sided figure. Both the square and the parallelogram are four-sided figure, hence they are quadrilateral.

Then length of each side of the square are same, hence opposite sides of a square are parallel. The length of opposite side of the parallelogram are parallel to each other. Hence both the square and parallelogram have opposite sides that are parallel.

             

Q4 No I do not agree with this statement. A parallelogram is a quadrilateral with two pairs of parallel sides. Even though the square is like that, there are also other shapes that fulfill these points. A few examples are rhombus, trapezium and rectangle. 

Q5 The opposite sides are the same and parallel to each other. The adjacent angles adds up to 180 degrees and the opposite angles are the same.Therefore, we can conclude that it is a parallelogram.

108's CLASSIFICATION OF QUADRILATERALS