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mLine 1:
Line 1: + + + − + + + − + − + − GIVEN :+ − + − + − + − + − + − − − − − PROOF : − − − − ar (BCE) = ar (ADF) = = − − ( Areas of Congruent figures are equal ) − − OBSERVATION / RESULT / OUTCOME : − − + − − ar (ABCD) = ar (BCE) + ar (ABED) − − <nowiki>= + =</nowiki> − − ar (ABEF) = ar (ABED) + ar (ADF) − − <nowiki>= + =</nowiki> − − Hence the theorem is verified. + + − Go back to the page - [[KVS Quadrilaterals|click here]]+
Parallelogram on same base and between same parallels have equal area (view source)
Revision as of 13:43, 19 December 2020
, 13:43, 19 December 2020added Category:Quadrilaterals using HotCat
=== Objectives ===
=== Objectives ===
To verify that Parallelograms on the same base and between the same parallels are equal in area
=== Estimated Time ===
=== Estimated Time ===
40 minutes
=== Prerequisites/Instructions, prior preparations, if any ===
=== Prerequisites/Instructions, prior preparations, if any ===
Knowledge about altitude, trapezium, congruent triangles, parallelogram and its area.
=== Materials/ Resources needed ===
=== Materials/ Resources needed ===
Click here to [[:File:Areas of parallelograms on the same base bwtween the same parallels.ggb|open]] the file
Digital : Click here to [[:File:Areas of parallelograms on the same base bwtween the same parallels.ggb|open]] the file
Non-digital : Paper, pencil, ruler, compass, protractor
=== Process (How to do the activity) ===
=== Process (How to do the activity) ===
{{Geogebra|kxre9cuf}}GEOMETRICAL VERIFICATION:
{{Geogebra|kxre9cuf}}'''Procedure :'''
# Draw AB ∥ FC and AB is the base.
# Draw Parallelograms ABCD and ABEF are on the same base AB and between same parallels AB and FC.
#Identifying plane figures on the same base and between the same parallels
AB ∥ FC and AB is the same base.
#Identify Congruent triangles i.e. Δ BCE ≅ Δ ADF and find the area of triangles
#Find the area of Trapezium ABED by using finding an area tool
Parallelograms ABCD and ABEF are
#What can you say about their areas?
#Proving that parallelograms on the same base and between the same parallels have equal area by using following calculations
on the same base AB and between
same parallels AB and FC.
Δ BCE ≅ Δ ADF (By SAS Congruence Criterion)
Area of the parallelogram ABCD
Area of the parallelogram ABCD
= Area of the Trapezium ABED + Area of the Triangle BCE
= Area of the Trapezium ABED + Area of the Triangle BCE
Area of the parallelogram ABEF
Area of the parallelogram ABEF
= Area of the Trapezium ABED + Area of the Triangle ADF
= Area of the Trapezium ABED + Area of the Triangle ADF
=== Evaluation at the end of the activity ===
=== Evaluation at the end of the activity ===
# If one rectangle and one parallelogram lying on the same base and between the same parallel lines then what will be area of the rectangle ?
Go back to the page - [[KVS Quadrilaterals|click here]]
[[Category:Quadrilaterals]]