Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the formula for the sum of interior angles of a polygon with n sides.
Perfect! For any polygon with n sides, the sum of interior angles is (n - 2) × 180°.
(2) State one property of the diagonals of a kite. Diagonals are
Excellent! The diagonals of a kite are perpendicular to each other.
(3) In a parallelogram, if one angle is 70°, find its adjacent angle.
Correct! Adjacent angles in a parallelogram are supplementary: 180° - 70° = 110°.
(4) Write the name of a quadrilateral with two pairs of adjacent sides equal.
Great! A kite has two pairs of adjacent sides equal.
(5) In a rectangle, if the length is 8 cm and the breadth is 6 cm, find the length of the diagonal.
Perfect! Using Pythagorean theorem:
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Prove that the sum of the interior angles of a quadrilateral is 360°.
(2) In a parallelogram, one angle is twice the adjacent angle. Find the measure of all the angles. The angles are:
Perfect! Opposite angles are equal in a parallelogram.
(3) Show that each diagonal of a rectangle divides it into two congruent triangles.
(4) In a kite, prove that one pair of opposite angles is equal.
(5) In a square, if the diagonal is 10 cm, find the length of each side. Side of square =
Perfect! Each side is
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Prove that the diagonals of a rhombus are perpendicular bisectors of each other.
(2) Prove that the opposite sides of a parallelogram are equal in length.
(3) In a parallelogram, the sum of the squares of the sides is equal to the sum of the squares of the diagonals. Prove this property.
(4) A quadrilateral is a parallelogram if one pair of opposite sides is both equal and parallel. Prove this statement.
(5) In a trapezium, the line joining the midpoints of the non-parallel sides is parallel to the bases and equal to half the sum of the lengths of the bases. Prove this.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The sum of the interior angles of a hexagon is:
(a) 540° (b) 720° (c) 900° (d) 1080°
Correct! For hexagon (n = 6): (6-2) × 180° = 4 × 180° = 720°.
(2) The diagonals of a kite are:
(a) Equal (b) Perpendicular (c) Equal and perpendicular (d) None
Correct! Kite diagonals are perpendicular but not necessarily equal.
(3) In a rectangle, the diagonals are:
(a) Unequal and perpendicular (b) Equal and bisect each other (c) Equal and perpendicular (d) None
Correct! Rectangle diagonals are equal and bisect each other but not perpendicular.
(4) Which quadrilateral has all sides equal but angles not equal to 90°?
(a) Square (b) Rhombus (c) Rectangle (d) Kite
Correct! A rhombus has all sides equal but angles are not necessarily 90°.
(5) In a parallelogram, if one angle is 60°, the opposite angle is:
(a) 60° (b) 120° (c) 90° (d) 100°
Correct! Opposite angles in a parallelogram are equal.
(6) A quadrilateral with opposite sides parallel and all angles 90° is:
(a) Square (b) Rectangle (c) Rhombus (d) Trapezium
Correct! A rectangle has opposite sides parallel and all angles 90°.
(7) The line joining the midpoints of the non-parallel sides of a trapezium is called:
(a) Median (b) Altitude (c) Diagonal (d) Midline
Correct! The midline of a trapezium joins midpoints of non-parallel sides.
(8) The diagonals of a parallelogram:
(a) Are equal (b) Bisect each other (c) Are perpendicular (d) None of these
Correct! Parallelogram diagonals always bisect each other.
(9) A quadrilateral having only one pair of equal opposite angles is:
(a) Square (b) Kite (c) Rhombus (d) Rectangle
Correct! A kite has only one pair of opposite angles equal.
(10) The diagonals of a rectangle intersect at:
(a) 45° (b) 60° (c) 90° (d) 30°
Correct! Rectangle diagonals are not necessarily perpendicular, but they bisect each other at any angle.
Let's classify advanced quadrilateral properties!!!
Excellent! You understand advanced quadrilateral properties perfectly.
True or False: Advanced Quadrilateral Properties
Determine whether these statements are True or False: