Activity 3 Proving Simple Geometrical Questions-Jaime (Q2,4,5)

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 

All of the above are correct.
A:Quadrilaterals are shapes with 4 sides.Squares and parallelogram both have 4 sides hence they are quadrilaterals.
B:Parallel lines are lines that are exactly straight in line to the line opposite it.This can be found in square since all sides are of equal length and in parallelogram since opposite sides are of equal length.
C:A trapezoid has only one pair of parallel line and the other sides of the trapezoid is not equal to each other.

Question 4:
‘All parallelograms are squares?’ Do you agree with this statement?
Justify your answer with example/s.
I do not agree with statement because parallelograms and squares are two different things.The square has all its sides equal in length,two pairs of parallel lines and forms right angles.However parallelogram on the other hand,has only the opposite sides of equal length,2 pairs of parallel lines and no right angles.Hence,a parallelogram is not a square instead is a completely different shape.

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.

Since ABCD is a parallelogram,BC and AD are parallel to each other and BA and CD in the same way is also parallel to each other.In this case,since E and F are the mid-points of AD and BC respectively,so when BFDE is formed ,F is the same distance away from C as E is away from A.In BFDE,F and E are diagonally opposite each other hence BE and FD are parallel to each other and a parallelogram is formed.

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