Difference between revisions of "Parallelogram on same base and between same parallels have equal area"
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=== Process (How to do the activity) === | === Process (How to do the activity) === | ||
− | {{Geogebra|kxre9cuf}} | + | {{Geogebra|kxre9cuf}}GEOMETRICAL VERIFICATION: |
+ | |||
+ | GIVEN : | ||
+ | |||
+ | AB ∥ FC and AB is the same base. | ||
+ | |||
+ | Parallelograms ABCD and ABEF are | ||
+ | |||
+ | on the same base AB and between | ||
+ | |||
+ | same parallels AB and FC. | ||
+ | |||
+ | PROOF : | ||
+ | |||
+ | Δ BCE ≅ Δ ADF (By SAS Congruence Criterion) | ||
+ | |||
+ | ar (BCE) = ar (ADF) = = | ||
+ | |||
+ | ( Areas of Congruent figures are equal ) | ||
+ | |||
+ | OBSERVATION / RESULT / OUTCOME : | ||
+ | |||
+ | Area of the parallelogram ABCD | ||
+ | |||
+ | = Area of the Trapezium ABED + Area of the Triangle BCE | ||
+ | |||
+ | ar (ABCD) = ar (BCE) + ar (ABED) | ||
+ | |||
+ | <nowiki>= + =</nowiki> | ||
+ | |||
+ | Area of the parallelogram ABEF | ||
+ | |||
+ | = Area of the Trapezium ABED + Area of the Triangle ADF | ||
+ | |||
+ | ar (ABEF) = ar (ABED) + ar (ADF) | ||
+ | |||
+ | <nowiki>= + =</nowiki> | ||
+ | |||
+ | Hence the theorem is verified. | ||
=== Evaluation at the end of the activity === | === Evaluation at the end of the activity === | ||
Go back to the page - [[KVS Quadrilaterals|click here]] | Go back to the page - [[KVS Quadrilaterals|click here]] |
Revision as of 10:27, 5 September 2020
Objectives
Estimated Time
Prerequisites/Instructions, prior preparations, if any
Materials/ Resources needed
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Process (How to do the activity)
Download this geogebra file from this link.
GEOMETRICAL VERIFICATION:
GIVEN :
AB ∥ FC and AB is the same base.
Parallelograms ABCD and ABEF are
on the same base AB and between
same parallels AB and FC.
PROOF :
Δ BCE ≅ Δ ADF (By SAS Congruence Criterion)
ar (BCE) = ar (ADF) = =
( Areas of Congruent figures are equal )
OBSERVATION / RESULT / OUTCOME :
Area of the parallelogram ABCD
= Area of the Trapezium ABED + Area of the Triangle BCE
ar (ABCD) = ar (BCE) + ar (ABED)
= + =
Area of the parallelogram ABEF
= Area of the Trapezium ABED + Area of the Triangle ADF
ar (ABEF) = ar (ABED) + ar (ADF)
= + =
Hence the theorem is verified.
Evaluation at the end of the activity
Go back to the page - click here