In triangle ABC, points M and N on sides AB and AC respectively

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsLong Answer Type

41. In a parallelogram ABCD, E and Fare the mid-points of sides AB and CD respectively. (see figure). Show that the line segments AF and EC trisect the diagonal BD.


322 Views

42. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. 
333 Views

43.

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 space equals space MA space equals space 1 half AB.

443 Views

 Multiple Choice QuestionsShort Answer Type

44. In triangle ABC, points M and N on sides AB and AC respectively are taken so that

AM equals 1 fourth AB space and space AN equals 1 fourth AC comma space Prove that MN = 1 fourth
113 Views

Advertisement
Advertisement

45. In triangle ABC, points M and N on sides AB and AC respectively are taken so that 

AM equals 1 fourth AB space and space AN equals 1 fourth AC comma space Prove space that space MN equals 1 fourth


Given: In triangle ABC, points M and N on the sides AB and AC respectively are taken so that

AM space equals 1 fourth AB space and space AN equals 1 fourth A C
To prove: MN equals 1 fourth BC.

Given: In triangle ABC, points M and N on the sides AB and AC respect

Construction: Join EF where E and F are the middle points of AB and AC respectively.
Proof: Y E is the mid-point of AB and F is the mid-point of AC.

therefore space space EF space parallel to space BC space and space space space space space space EF equals 1 half BC space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
space space space Now comma space space space space space space space space space space space space space space space space space space space AE equals 1 half AB
space space space and space space space space space space space space space space space space space space space space space space space space AM equals 1 fourth space AB
therefore space space space space space space space space space space space space space space space space space space space space space space space space space AM space equals space 1 half AE
Similarly comma space space space space space space space space space space space space space space space space AN space equals space 1 half space AF
rightwards double arrow space space M and N are the mid-points of AE and AF respectively.

therefore space space MN space parallel to space EF space and space MN space equals space 1 half space EF equals 1 half open parentheses 1 half BC close parentheses
                                                             | From (1)
                                             equals space 1 fourth space BC.
                           
 
280 Views

Advertisement
46. ABCD is a rhombus and AB is produced to E and F such that AE = AB = BF. Prove that ED and FC are perpendicular to each other.
1943 Views

 Multiple Choice QuestionsLong Answer Type

47. In ∆ABC, AD is the median through A and E is the mid-point of AD. BE is produced to meet AC in F. Prove that  AF equals 1 third AC
203 Views

48.

D, E, F are respectively the midpoints of the sides BC, CA and AB of a triangle ABC. Show that:
(i) BDEF is a parallelogram
(ii) DFEC is a parallelogram.

470 Views

Advertisement

 Multiple Choice QuestionsShort Answer Type

49. In the figure ABCD is a parallelogram and E is the mid-point of side BC. DE and AB on producing meet at F. Prove that AF = 2AB.


233 Views

 Multiple Choice QuestionsLong Answer Type

50. ABCD is a trapezium in which side AB is parallel to the side DC and E is the mid-point of side AD (see figure). If F is a point on the side BC such that the segment EF is parallel to the side DC, prove that F is the mid-point of BC and EF = 1 half (AB + DC).


5399 Views

Advertisement