Activity 3 - eLearning Maths

Hi Mr Jo, can you help me to delete my previous post? It was too dark to be seen! =D

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:

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 : Yes, the statement is justified by the statement which the Mentor mentioned, "A rhombus is a parallelogram, but all four sides have the same length."

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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 ) All the above

Examples : A ) A square and parallelogram have four sides, so they are considered as quadrilaterals.

     B ) A square and parallelogram must have sides that are parallel, otherwise, they aren't even considered as squares        and parallelograms anymore.

      C ) The top side and the bottom side of the trapezoid are parallel.

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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.

¹ sum of two angles equals 180⁰

Answer : This figure is a trapezoid as the top and the bottom lines are parallel, but not of equal lengths

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Question 4:

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

Answer : No, I do not agree with this statement as squares require all sides to be of the same length, whilst not all parallelograms have all sides which are of the same length.

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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 : BC and AD are parallel, so a portion of them (BF and ED) would also be parallel. Lines BF and ED's corners are the same angle, as BF and ED are an equal distance apart, so this shows that they are parallel.

Done by : See To Yu Xiang, s1-09, 20

Activity 3 - eLearning Maths

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:

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 : Yes, the statement is justified by the statement which the Mentor mentioned, "A rhombus is a parallelogram, but all four sides have the same length."

---

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 ) All the above

Examples : A ) A square and parallelogram have four sides, so they are considered as quadrilaterals.

     B ) A square and parallelogram must have sides that are parallel, otherwise, they aren't even considered as squares        and parallelograms anymore.

      C ) The top side and the bottom side of the trapezoid are parallel.

---

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.

¹ sum of two angles equals 180⁰

Answer : This figure is a trapezoid as the top and the bottom lines are parallel, but not of equal lengths

---

Question 4:

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

Answer : No, I do not agree with this statement as squares require all sides to be of the same length, whilst not all parallelograms have all sides which are of the same length.

---

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 : BC and AD are parallel, so a portion of them (BF and ED) would also be parallel. Lines BF and ED's corners are the same angle, as BF and ED are an equal distance apart, so this shows that they are parallel.

Done by : See To Yu Xiang, s1-09, 20

Proving Simple Geometrical Questions 2,4 and 5 by Niklaus Teo

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: A and B

Explanation:

A: A quadrilaterals means that a shape has 4 sides, the sides must be straight and it must be 2D. A square and parallelogram both comply to this.

B: A square and parallelogram have 2 pairs of parallel lines.

Question 4:

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

Ans: No, i do not agree. A square consist equal sides and every angle is a right angle. Although a parallelogram have equal sides, but only the opposite angles are equal, which means that not all angles are equal

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: BFDE is a parallelogram, because F is placed in the mid point of BC and E is placed in the mid point of AD. Since AD and BC are equal lengths, that means that FB and ED are equal in length. With FD and BE being straight lines, this proves that BFDE is indeed a parallelogram.

Question 1, 3, 4 Gwendolyn Chee

1) This statement is true because the definition of a rhombus is all of its opposite sides are parallel to each other. A square fits that criteria but to be considered a square is for all four corners to be at a 90 degree angle, which cannot be guaranteed in a rhombus. 

3) This figure is a trapezium. A trapezium has one set of opposite lines parallel to each other, a pair of lines not parallel to each other and has a pair of opposite angles that are supplementary.

4) Not all parallelograms are squares. But all squares are parallelograms. Squares have four sides where two opposite sides are parallel to each other. But parallelograms do not always have four equal sides.

Questions 1,3 and 5

Q1.) The statement is true. { 'A square is a rhombus but a rhombus is not a square'. }

A square is a special kind of rhombus. In fact, a square is also a special kind of rectangle. Just like the rhombus which is a special kind of parallelogram, the rectangle is also a special kind of parallelogram thus the rhombus is also a special kind of parallelogram.

"A square is a special kind of rhombus." Why is this so?

This is because the square has 4 equal sides like the rhombus but the special feature of the square is that every angle in it is a right angle.

'A square is a rhombus but a rhombus is not a square'  [Proved]

Q3.)It is a trapezium.

A trapezium has only one pair of side which are parallel and the other two are not.

5.)If ABCD is a parallelogram, and if E is midpoint of AD and  F is midpoint of BC, BFDE must be a parallelogram. This is because BF and ED are equal and parallel.

Question 3, 4, and 5 by Lee Si Yuan

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.

1sum of two angles equals 180 degrees.

Ans: This quadrilateral is a trapezium. The definition of a trapezium is that it has at least one set of parallel lines, without considering the fact whether the length of the lines are equal, or if the other two lines are parallel to each other or they must be of a certain length.

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

Ans: No, I do not agree that all parallelograms are squares. The definition of square is that it must have all four of its corners at a right angle, and not all parallelograms meets this criteria.

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 criteria of a parallelogram is that there must be 2 pairs of parallel lines. Since BF has the same length as ED, and they are parallel to each other, BE and FD should also be of the same length and are parallel to each other. Hence BFDE must be a parallelogram.


Si Yuan

Answers for Math E-learning Activity 3 (Cherin)

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:

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

 

-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.

-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

 

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Question 4:

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

 

-No, not all parallelograms are squares. Square must have its corners at a right angle, but not all parallelograms fulfil 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.

 

-BF has the same length as ED, and as they are parallel to each other, BE and FD are also of the same length and are parallel to each other.