Hg

Name: Class 9

___________________________________________________________________________________________________________________________________

The Hg Classes (8

th

to 12

th

) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.

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AREA of PARALLELOGRAMS and TRIANGLES

1.

Two congruent figures always have same area, but two figures having same area may or may not be

congruent.

2.

on the same base (or equal bases) and between

same ||s parallels have equal area.

ar (ABCD) = ar (EFCD)

Converse: Parallelograms on the same base (or equal bases)

and having equal area lie b/w same parallels.

Same Base = CD; Same ||s = CD & AF

3.

Area of = Base x Corresponding Altitude; Area of = ½ x Base x Corresponding Altitude.

4.

If a and a are on the same base and between same

||s, then area of the triangle is ½ the area of the

parallelogram.

ar (ABP) = ½ ar (ABCD)

Same Base = AB; Same ||s = AB & PC

5.

on the same base (or equal bases) and between the

same ||s are equal in area.

ar (ABD) = ar (ABC)

Converse: Triangles on the same base (or equal bases) and

having equal area lie b/w same parallels.

Same Base = AB; Same ||s = AB & EF

6.

Diagonal of a divides it into two triangles of equal area.

ar (ABD) = ar (CDB)

7.

Median of a triangle divides it into two triangles of equal

area.

If AD is median in △ABC, then

ar (ABD) = ar (ADC)