Important Questions for CBSE Class 9 Mathematics Quadrilaterals Chapter 8

Important Questions for CBSE Class 9 Mathematics Quadrilaterals

Chapter 8

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS
Question.1 Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral.
Solution.

Question.2 Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?
Solution.

Question.3 If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.
Solution.

Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram. [CBSE-15-6DWMW5A]
Solution.

Question.5

Solution.

Question.6.If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral.
Solution. Rhombus.

Question.7 In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S.
Solution.

Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
Solution.

Question.9 In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.

Solution.

Question.10 If the diagonals of a parallelogram are equal, then state its name.
Solution. Rectangle

Question.11 ONKA is a square with ∠KON = 45°. Determine ∠KOA.
Solution.

Question.12 PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.
Solution.

Question.13

Solution.

Question.14

Solution.

Question. 15.If ABCD is a parallelogram, then what is the measure of ∠A – ∠C ?
Solution. ∠A –∠C = 0° [opposite angles of parallelogram are equal]

SHORT ANSWER QUESTIONS TYPE-I
Question.16 Prove that a diagonal of a parallelogram divide it into two congruent triangles. [CBSE March 2012]
Solution. Given : A parallelogram ABCD and AC is its diagonal.

Question.17 ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see fig.). Show that :
(i) AAPB ≅ ACQD (ii) AP = CQ            [CBSE March 2012]
Solution.

Question.18

Solution.

Question.19

Solution.

Question.20

Solution.

Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]
Solution.

Question.22 ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. Show that AX\\CY. D x c
Solution.

SHORT ANSWER QUESTIONS TYPE-II
Question.23

Solution.

Question.24 ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that : [CBSE-15-6DWMW5A]
Solution.

Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]
Solution.

Question.26 D, E and F are respectively the mid-points of the sides AB, BC and CA of a triangle ABC. Prove that by joining these mid-points D, E and F, the triangles ABC is divided into four congruent triangles. [NCERT Exemplar Problem]
Solution.

Question.27

Solution.

Question.28

Solution.

Question.29

Solution. Since line segment joining the mid-points of two sides of a triangle is half of the third side. Therefore, D and E are mid-points of BC and AC respectively.

LONG ANSWER TYPE QUESTIONS
Question.30 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC ad D. Show that:
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = 1/2 AB. [CBSE March 2012]
Solution.

Question.31

Solution.

Question.32 The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
Solution.

Question.33

Solution.

Question.34

Solution.

Question.35 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC at D. Show that:
(i) D is the mid-point of AC
(ii) MD⊥ AC
(iii) CM = MA =1/2 AB. [CBSE March 2012]
Solution.

Question.36

Solution.

Question.37 ABCD is a rhombus. Show that diagonals AC bisects ∠A as well as ∠C and diagonal BD bisects∠B as well as ∠D
Solution.

Question.38

Solution.

Question.39

Solution. Here, in AABC, R and Q are the mid-points of AB and AC respectively.

Question.40

Solution.

Question.41

Solution.

Question. 42 ABCD is a parallelogram in which diagonal AC bisects∠A as well as ∠C. Show that ABCD is a rhombus. [CBSE-14-17DIG1U]
Solution.

Question. 43

Solution.

Question.44 ABCD is a parallelogram. If the bisectors DP and CP of angles D and C meet at P on side AB, then show that P is the mid-point of side AB. [CBSE-15-NS72LP7]
Solution.

Value Based Questions (Solved)

Question.1

Solution.

Question.2

Solution.

Question.3

Solution.