Q1.
Which of the following figures lie on the same base and between the same
parallels? In such a case write the common base and the two parallels.
Q2.
In a parallelogram
to the sides
Q3.
it is given that
and the altitude corresponding
are
Calculate the area of the given trapezium
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, respectively. Find
.
.
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Q4.
Calculate the area of the quadrilateral
Q5.
In the given figure,
Q6.
The diagonals
in the given figure.
is a parallelogram and
of a quadrilateral
is any point on
intersect at
. Prove that
and separate it into
four triangles of equal area. Show that the quadrilateral is a parallelogram.
Q7.
The side of
parallel to
of a parallelogram
meets
Show that
Q8.
produced in
is produced to any point . A line through
and the parallelogram
.
In the given figure, two parallelograms
of
. Prove that
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completed.
are drawn o opposite sides
.
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Q9.
A rectangle is formed by joining the mid-point of the sides of a rhombus. Show
that the area of the rectangle is half the area of the rhombus.
Q10.
The diagonals of a parallelogram
intersect
and
intersect at a point
. Show that
, a line is drawn to
divides the parallelogram into two parts
of equal area.
Q11.
In the figure
Q12.
In the given figure,
opposite sides of
, prove that
are on the same base
such that
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with
Show that
on
bisects
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Q13.
In the given figure
is parallelogram and
is any point on the diagonal
.
Show that
Q14.
D is the mid-point of side
point of
Q15.
of
is the mid-point of
, if
is the mid-
prove that
The given figure shows a pentagon
.
is parallel to
is parallel to
. Show that
Q16.
In the figure, the diagonal
of a quadrilateral
intersect at
. If
, prove that
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Q17.
In the given figure,
a point on
is the median of
and
is
. Prove that
(i)
(ii)
Q18.
The vertex
of
is joined to a point
on the side
. The mid-point of
is
. Prove that
Q19.
In the given figure, the point
divides the side
of
in the ratio
Prove
that
Q20.
The base
of
is divided by
such that
.Prove that
.
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Page 5 of 7
Answers
A1.
(i)
and trapezium
same base
(ii) Parallelogram
and
the same base.
(iii) Parallelogram
and trapezium
the same parallels.
(iv)
and parallelogram
same parallels
and same parallels
lie between the same parallels
on the same base
are on the same base
.
but not on
but not between
and between the
.
A2.
A3.
A4.
A5.
Hint: Draw
A6.
Hint: Show that
A7.
and use the property.
“Triangles on the same base and having equal area lie between the same
parallels.”
Hint: Using property: “Triangles on the same base and between same parallels
are equal in area.” Show that
. Now using the properties of a
A8.
parallelogram get the required result.
Hint: Show that
and use the property: “Two congruent figures have
A9.
equal areas.”
Hint: Join
and use the property: “if a parallelogram and a triangle are on the
A10.
same base and between the same parallels, then are of the triangle is half the area
of the parallelogram.”
Hint: Show that
and use the property “Two congruent figures have
A11.
equal areas.” Now use the properties of parallelogram to get the required result.
Hint:
are on the same base and between the same parallels. Add
on both sides.
A12.
Hint: Draw
. Show that
and get the required
result.
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Page 6 of 7
A13.
Hint: Join
. Since diagonals of a parallelogram bisect each other implying that
is mid-point of
of
. This also implies that
is median of
and
is median
.
A14.
A15.
Hint: Median of a triangle divides it into two triangles of equal areas.
Hint: Use the property “Triangles on the same base and between the same
parallels are equal in area” to show
A16.
A17.
Hint: Median of a triangle divides it into two triangles of equal area.
Hint: Hint: Median of a triangle divides it into two triangles of equal areas.
are medians of
respectively.
A18.
Hint: Median of a triangle divides it into two triangles of equal area.
A19.
Hint:
A20.
result.
Hint:
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simplify and substitute the values to prove the required
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