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,
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.]
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
Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.