# Ncert Solutions For Class 9 Maths Chapter 8 Quadrilaterals

quadrilaterals class 9 ncert solutions, quadrilaterals worksheet, properties of quadrilaterals worksheet, types of quadrilaterals worksheet, worksheets on quadrilaterals, classifying quadrilaterals worksheet, quadrilaterals worksheets, classifying quadrilaterals worksheets, identifying quadrilaterals worksheet, area of quadrilaterals worksheet, triangles and quadrilaterals worksheet, geometry quadrilaterals worksheet, classify quadrilaterals worksheet, special quadrilaterals worksheet, polygons , ncert solutions, chapter 8,chapter 8ncert solutions, quadrilaterals ncert solutions, ncert solutions for class 9 maths, class 9 maths ncert solutions, ncert solutions for class 9, ncert class 9 maths, class 9 maths, class 9 maths solution, ncert solutions class 9, class 9 maths , ncert class 9,

## In this pdf file you can see answers of following Questions

### EXERCISE 8.1

Question 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Question 2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Question 3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Question 4.
Show that the diagonals of a square are equal and bisect each other at right angles.

Question 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Question 6. Diagonal AC of a parallelogram ABCD bisects ∠ A (see Fig. 8.19). Show that
(i) it bisects ∠ C also
(ii) ABCD is a rhombus.

Question 7. ABCD is a rhombus. Show that diagonal AC bisects ∠ A as well as ∠ C and diagonal BD bisects ∠ B as well as ∠ D.

Question 8.
ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that:
(i) ABCD is a square
(ii) diagonal BD bisects ∠ B as well as ∠ D.

Question 9. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:
(i) Δ APD Δ CQB
(ii) AP = CQ
(iii) Δ AQB Δ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram

Question 10.
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that :
(i) Δ APB Δ CQD
(ii) AP = CQ

Question 11.
In Δ ABC and Δ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that :
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) Δ ABC Δ DEF.

Question 12. ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that:
(i) ∠ A = ∠ B
(ii) ∠ C = ∠ D
(iii) Δ ABC Δ BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

### EXERCISE 8.2

Question 1. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that :
(i) SR || AC and SR = 1 2 AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.

Question 2. ABCD is a rhombus and P, Q, R and S are ©wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Question 3. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Question 4. ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

Question 5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

Question 6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Question 7. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and 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

Please Wait pdf file is loading (कृपया इंतजार करें pdf file लोड हो रही है)...
Loading speed will depend up on your download speed. Pdf file के लोड होने में लगा समय आपकी डाउनलोड स्पीड पर निर्भर करेगा

 Page of

उपर दिखायी दे रही पीडीऍफ़ को डाउनलोड करने का लिंक नीचे दिया गया है

### NCERT Books for Class 1- 12 Hindi & English Medium

 Mathematics Biology Psychology Chemistry English Economics Sociology Hindi Business Studies Geography Science Political Science Statistics Physics Accountancy

### Solved Last Year Question Paper

If You have any problem/query related to above page please send us your Query to [email protected] with code Serial No1454/1101. Thanks