Prove that the parallelograms on the same base and between the same parallels are equal in area by paper cutting and pasting method
Answers
Answer:
To show that the parallelograms on the same base and between the same parallel lines are equal in area by paper cutting and pasting. Area of parallelogram = base x height.
Objective
To show that the parallelograms on the same base and between the same parallel lines are equal in area by paper cutting and pasting.
Prerequisite Knowledge
Area of parallelogram = base x height.
Shortest distance between two parallel lines is the perpendicular distance between parallel lines and it remains same for that pair of parallel lines.
Materials Required
Glazed paper, a pair of scissors, gluestick, geometry box.
Procedure
Draw a parallelogram by paper folding activity.
Cut this parallelogram using scissors and name it as ABCD, [fig.(i)].
Mark any point E on DC.
From A fold the parallelogram till the point E (any point on DC). A crease AE is formed, fill another colour in ∆ADE. [fig. (ii)].
Cut the parallelogram ABCD along AE to get ∆AED.
Paste the ∆AED on the other side along BC of parallelogram ABCD as shown in fig. (iii).
Cut the parallelogram ABCD along AE to get ∆AED.
Paste the ∆AED on the other side along BC of parallelogram ABCD as shown in fig. (iii).We get new parallelogram AEPB.
Observation
We observe that the two parallelograms ABCD and ABPE have same base AB.
Two parallelograms lie between same parallel lines, i.e., AB and CD and height between them is same at all points.
By formula, area of parallelogram = base x height
ar(||gm ABCD) = AB x EH
ar(||gm ABPE) = AB x EH
Result
We have verified that two parallelograms lying on same base and between same parallel lines are equal in area.
Learning Outcome
Students follow that the parallelograms on the same base and between the same parallels have same area.
Activity Time
This theorem can be proved by using a graph paper. Students will try this and verify the theorem.
Prove that areas of a rectangle and a square of same height and on the same base are equal by using paper cutting and pasting method.
