Q1.
Prove that the sum of the angles of a quadrilateral is
Q2.
The four angles of a quadrilateral are in the ratio
Q3.
Find the measure of angle
Q4.
Find the measure of .
Q5.
Prove that the sum of exterior angles of a quadrilateral is
Q6.
Three angles of a quadrilateral are equal and the measure of the fourth angles is
. Find the measure of each of the equal angles.
Q7.
In the given figure, the bisectors of
If
Q8.
Q9.
Q10.
.
. Find the angles.
for the following quadrilateral.
meet in a point
.
.
, find the measure of
Prove that in a parallelogram, the opposite sides are equal and the opposite angles
are equal.
Prove that diagonals of a rhombus bisect each other angles.
Two adjacent angles of a parallelogram are as
. Find the measure of each of its
angles.
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Q11.
In the given figure,
is a parallelogram,
respectively. Prove that
Q12.
and
. Find the
and hence find the measure of each of its angles.
In the given figure,
the angles
Q14.
.
Two adjacent angles of a parallelogram are
value of
Q13.
are the bisectors of
is a parallelogram and line segments
respectively. Show that
bisect
.
Q16.
Prove that the diagonals of a square are equal and bisect each other at right
angles.
If an angle of a parallelogram is two–third of its adjacent angel, then what is the
smallest angle of the parallelogram?
The lengths of diagonals of a rhombus are
. Find the length of
Q17.
each side of the rhombus.
The length and breadth of a rectangle are in the ratio
Q15.
measure
. If the diagonals
, then what is the perimeter of the rectangle?
Q18.
If one angle of a parallelogram is
less than twice the smallest angle, then
Q19.
Q20.
what is the largest angle of the parallelogram?
Prove that any two adjacent angles of a parallelogram are supplementary.
The sides of a rectangle are in the ratio
and its perimeter is
. Find its
length and breadth.
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Answers
A1.
Hint: Divide it into
triangles and add the angles.
A2.
A3.
A4.
A5.
A6.
Hint: Show that interior and exterior angle from a supplementary pair.
A7.
A8.
A9.
A10.
A11.
Hint: Draw a diagonal and use properties of transversal cutting the two parallel
lines.
Hint: Draw both diagonals and in the triangles so formed, prove SSS congruence.
Hint: The sum of two adjacent angles of a parallelogram is
,
. Therefore, take
. Then, consider
, and use
the angel sum property of a triangle.
A12.
A13.
A14.
Hint: Show congruency of
. Thus prove that
is a
parallelogram.
Hint: Use the result that every square is a rectangle and hence use the diagonal
properties of rectangles. Then consider that every square is a rhombus and
consider the diagonal properties of the rhombus.
A15.
A16.
A17.
A18.
A19.
Hint: Use the property of parallel lines: sum of interior angles on the same side of
the transversal which is cutting two parallel lines is
.
A20.
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