In this page 10th grade geometry worksheet2 we are going to see some practice questions. You can try the below problems on your own. If you find it difficult to do any problems you can just click the solution link to get detailed solution.

(9) In a triangle ABC,AD is the internal bisector of angle A, meeting BC at D.

(i) If BD = 2 cm, AB = 5 cm, DC =3 cm find AC.     solution

(ii) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm find BC.  solution

(iii) If AB = x, AC = x – 2 cm, BD = x + 2 cm and DC = x – 1 find the value of x
solution

(10) Check whether AD is the bisector of angle A of the triangle ABC in each of the following.

(i) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm   solution

(ii) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 3 cm    solution

 (11) In a triangle MNO, MP is the external bisector of angle M meeting NO produced at P. IF MN = 10 cm, MO = 6 cm, NO - 12 cm, then find OP.  Solution

(12) In a quadrilateral ABCD, the bisectors of ∠B and ∠D intersect on AC at E. Prove that (AB/BC) = (AD/DC).  Solution

(13) The internal bisector of ∠A of triangle ABC meets BC at D and the external bisector of ∠A meets BC produced at E. Prove that (BD/BE) = (CD/CE).  Solution

(14) ABCD is a quadrilateral with AB = AD. If AE and AF are internal bisectors of ∠BAC and ∠DAC respectively,then prove that the sides EF and BD are parallel.