eLearning- Questions 3, 4 and 5 by Hardy Shein Nyein Chan

Q3)

Ans: I identified the shape as a trapezium. Due to the fact that majority of trapeziums have one pair of parallel lines although not the same and one pare that is not. Thus, it fits the criteria in the question that the figure is a trapezium.

Q4)

Ans: No, I do not agree with the statement, ‘All parallelograms are squares?’. One can say that the square is a parallelogram as the square fits the criteria of the parallelogram. The square has two pairs of opposite sides that are parallel and and equal to each other. However, the parallelogram( in majority) does not have all four equal sides( unlike the square) and all of their angles are not right-agles while the square does.

Q5)

Ans: BFDE is a parallelogram. It has the characteristics of a parallelogram. It has two different pairs of opposite sides that are parallel to each other and equal in length. Thus, having fit the criteria to match a parallelogram, one can say that BFDE is a parallelogram.

Question 2, 4, 5

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

  The answer is D. For A, quadrilaterals are 2-dimensional figures with 4 straight sides, and the interior angles add up to 360 degrees. Examples of quadrilaterals are squares, parallelograms, and kites. Since a square and a parallelogram are 2-dimensional figures with 4 straight sides, and the interior angles add up to 360 degrees, they are quadrilaterals. For B, squares have 2 pairs of parallel lines, while a parallelogram has a pair of parellel line at each side. Hence, opposite sides of a square and a parallelogram are parallel. For C, a trapezoid has only a pair of parellel lines. If there were more than a pair of parallel lines, it would be a parallelogram. So, all of the statements are correct.

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

Justify your answer with example/s.

  No, not all parallelograms are squares. Some parallelograms have internal angles which are not all 90 degrees, while all squares have 4 angles with 90 degrees. Also, a pair of lines of a parallelogram would have a different length than the other pair of lines. All of the squares' lines are equal in length, which proves again that not all parallelograms are squares.

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.

 A parallelogram is a figure with 2 pairs of parallel lines. Since figure BFDE has 2 pairs of parellel lines, it is a parallelogram.

Preston

Question 5 by Chio Jia Le

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: As lines BE and FD cut through the midpoints of AD and BC respectively, the 2 lines are said to be parallel to each other. With lines BF and ED already proven to be straight and parallel sides, BFDE must be a parallelogram.

Question 2 by Chio Jia Le

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 of the above 

ANSWER: D, all of the above statements. Firstly, let's start with justifying A. A square and parallelogram are quadrilaterals as they fulfill the properties of it, which is 2-dimensional closed shape with four straight sides. Next, opposite sides of a square and a parallelogram are parallel. This is true as these 2 shapes have 2 pairs of opposite sides parallel. Lastly, a trapezoid has one pair of parallel sides. I agree with this statement as a trapezium has one pair of opposite sides parallel and

non-parallel equal sides.

Question 1 by Chio Jia Le

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: A square has all the rhombus' properties while the rhombus do not have all of the square's property. For example, a square's adjacent sides are perpendicular to each other while the rhombus' are not perpendicular. Another property is that the length of diagonals of the square are equal but the rhombus' are not the same.

Activity 3-Proving Simple Geometrical Questions

1.'A square is a rhombus but a rhombus is not a square'.
Ans: It is true.

These are both rhombuses:

  +--------+
  |        |        +--------+
  |        |       /        /
   |        |      /        /
  |        |     /        /
  +--------+    +--------+

But only this is a square:

  +--------+
  |        |
  |        |
  |        |
  |        |
  +--------+
 

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. Quadrilaterals means four sides and a square and a parallelogram have four sides. Since their opposite angles are equal, thus the sides of a square and a parallelogram are equal. Yes, a trapezoid has one pair of parallel side as shown in the picture below.

 

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

Justify your answer with example/s.

Ans: I agree with the statement.The interior angles of a parallelogram aren't necessarily 90 degrees. All fours side are not necessarily equal in a parallelogram.

elearning 2010 : Everyday Quadrilaterals

posted by Mr Johari
Learning Objective (Activity 2)

In this learning activity, you will demonstrate your understanding of the properties quadrilateral by identifying objects around us that exhibit these shapes.

Instructions

1. Choose 2 out of the 3 special quadrilaterals - parallelogram, trapezium and kite.
2. Find objects at home that exhibit the shape of these 2 selected quadrilaterals.
3. Take a photo of each object and post them on the Wall Wisher at the class Maths blog