Difference between revisions of "Parallelogram on same base and between same parallels have equal area"

Revision as of 10:27, 5 September 2020

Click here to open the file

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.

Go back to the page - click here

@@ Line 9: / Line 9: @@
 === 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 ===
 Go back to the page - [[KVS Quadrilaterals|click here]]