Page 169 - Maths Skills - 8

Understanding Quadrilaterals 167

C. Write ‘T’ for true and ‘F’ for false statements E. Assertion-Reason Based Questions

1. A square is not a rhombus. Directions for Questions 1 to 2: In each of the
questions given below, there are two statements
2. Every rhombus is not a kite. marked as Assertion (A) and Reason (R). Mark your
answer as per the codes provided below:
3. Every rectangle is a parallelogram.
(a) Both A and R are true and R is the correct
4. The diagonals of a parallelogram bisect each explanation of A.
other. (b) Both A and R are true but R is not the correct
explanation of A.
5. The diagonals of a square bisect each other at
right angles. (c) A is true but R is false.
(d) A is false but R is true.

D. Case Study Based Questions Q. 1. Assertion (A): A quadrilateral can have all sides
During math lab activity each student was given four of different lengths and still be a parallelogram.
broomsticks of lengths 6 cm, 6 cm, 5 cm, 5 cm to Reason (R): A parallelogram has two pairs of
make different types of quadrilaterals. opposite sides parallel to each other.
Answer the following questions on the basis of the Q. 2. Assertion (A): The sum of the measures of all
above data. the four angles of a rectangle is 360°.

1. How many quadrilaterals can be formed using Reason (R): A rectangle is a polygon with four
these sticks? sides and four vertices.

(i) Only one type of quadrilateral can be
formed. SUBJECTIVE TYPE QUESTIONS

(ii) Two type of quadrilateral can be formed. F. Solve the following word problems
(iii) Three type of quadrilateral can be formed. 1. In a convex hexagon, prove that the sum of all
(iv) Four type of quadrilateral can be formed. the interior angles is equal to twice the sum of its

2. Name the quadrilaterals formed. exterior angles formed by producing the sides in
the same order.
(i) Rectangle, kite, square 2. The sum of the interior angles of a polygon
(ii) Square, parallelogram, rectangle is three times the sum of its exterior angles.
(iii) Rectangle, parallelogram, kite Determine the number sides of the polygon.

(iv) Square, kite, parallelogram 3. Find the number of sides of a polygon whose
3. In a trapezium ABCD, AB||CD and ∠A = ∠B = 45°, exterior and interior angles are in the ratio 1 : 5.
the teacher asked the students to find ∠D 4. ABCD is a square. AC and BD intersect at O.
(i) 105° (ii) 135° D C Find the measure of ∠DOC.
(iii) 130° (iv) 120° A B

HOTS

1. Hariti walked diagonally across a park. Yukti walked along the length and breadth of the park. The park is
30 metres wide and 40 metres long. How much more did Yukti walk than Hariti?

2. Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measure
of their interior angles is 3 : 4. Find number of sides of each polygon.