Answer:
• A simple closed curve made up of only line segments is called a
polygon.
• A diagonal of a polygon is a line segment connecting two non-
consecutive vertices.
• A convex polygon is a polygon in which no portion of its any
diagonal is in its exterior.
• A quadrilateral is a polygon having only four sides.
• A regular polygon is a polygon whose all sides are equal and also
all angles are equal.
• The sum of interior angles of a polygon of n sides is (n-2) straight
angles.
• The sum of interior angles of a quadrilateral is 360°.
• The sum of exterior angles, taken in an order, of a polygon is 360°.
• Trapezium is a quadrilateral in which a pair of opposite sides is
parallel.
• Kite is a quadrilateral which has two pairs of equal consecutive
sides.
• A parallelogram is a quadrilateral in which each pair of opposite
sides is parallel.
• A rhombus is a parallelogram in which adjacent sides are equal.
• A rectangle is a parallelogram in which one angle is of 900.
• A square is a parallelogram in which adjacent sides are equal and
one angle is of 900.
• In a parallelogram, opposite sides are equal, opposite angles are
equal and diagonals bisect each other.
• In a rhombus diagonals intersect at right angles.
• In a rectangle diagonals are equal.
• Five measurements can determine a quadrilateral uniquely.
• A quadrilateral can be constructed uniquely if the lengths of its
four sides and a diagonal are given.
• A quadrilateral can be constructed uniquely if the lengths of its
three sides and two diagonals are given.
• A quadrilateral can be constructed uniquely if its two adjacent
sides and three angles are given.
• A quadrilateral can be constructed uniquely if its three sides and
two included angles are given.
In examples 1 to 8, there are four options out of which one is correct.
Write the correct answer.
Example 1 : The number of diagonals in a polygon of n sides is
(a)
n n( 1)
2
(b)
n n( 2)
2
(c)
n n( 3)
2
(d) n (n–3).
Solution : The correct answer is (c).
Example 2 : The angles of a quadrilateral ABCD taken in an order are
in the ratio 3 : 7 : 6 : 4. Then ABCD is a
(a) kite (b) parallelogram
(c) rhombus (d) trapezium
Solution : The correct answer is (d).
Step-by-step explanation:
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