Parallelograms on the same base and between
the same parallels are equal in area.
and are two
(Corresponding angles, ,and AF transversal.)
angles, , and transversal.)
of the triangles, by angle sum property)
(Opposite sides of parallelogram )
Theorem 2: Area of triangle is half of parallelogram
with common base and between same parallel.
parallelogram be with
common base .
To prove :
Construction: Draw , .
Extend Up to .
between two parallel lines is equal)
3: Two triangles on the same base (or
equal bases) and between the same parallels are equal in area.
And be two triangles
with common base and between same
Construction: Draw , and ,
Let line meets at and at .
(Triangle and parallel
gram with common base and
Between parallel lines) …(1)
Both the parallelogram have same base and
between two parallel lines,
Theorem 4 : Two triangles having the same base and equal
areas lie between the same
and have equal
Triangles lie between two parallel
corresponding heights are equal, we say point and lie on
the line parallel
to , through .