Friday, August 13, 2010

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


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.

1 comment:

  1. Hi Niklaus,

    The comment I am going to give you is on question 2. For the answer you gave clear evidence and support to justify your answer. At the same time using the properties of quadrilaterals to explain that the statement is wrong, allowing you to revisit the properties of some quadrilaterals. Process wise it looks like you stated what and why in the question simply without too much or too little explanation for us to understand easily. :)

    KJ Shakti