10th Grade Geometry Solution4

In this page 10th grade geometry solution4 we are going to see solutions of some practice questions.

(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:

Using “Angle bisector theorem” in the triangle ABC, we get

(AB/AC) = (BD/DC)

(5/AC) = (2/3)

AC = (3 x 5)/2

      = 15/2

      = 7.5 cm      


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

Using “Angle bisector theorem” in the triangle ABC, we get

(AB/AC) = (BD/DC)

(5.6/6) = (BD/3)

BD = (5.6 x 3)/6

       = 16.8/6

       = 2.8 cm

From this we need to find the value of BC

 BC = BD + DC

      = 2.8 + 3

.    = 5.8 cm  


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

Using “Angle bisector theorem” in the triangle ABC, we get

(AB/AC) = (BD/DC)

[x/(x – 2)] = [(x + 2)/(x - 1)]

x (x – 1) = (x + 2) (x – 2)

x ² – x = x ² – 4

x² – x - x² + 4 = 0

   - x + 4 = 0

   - x = - 4

     x = 4 cm

The value of x is 4 cm


(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:

To check whether AD is the bisector of angle A of the triangle ABC, we have to check the following condition

(AB/AC) = (BD/DC)

(4/6) = (1.6/2.4)

0.66 = 0.66

From this we come to know that AD is the bisector of angle A of the triangle ABC.


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

Solution:

To check whether AD is the bisector of angle A of the triangle ABC, we have to check the following condition

(AB/AC) = (BD/DC)

(6/8) = (1.5/3)

0.75 ≠ 0.5

From this we come to know that AD is not the bisector of angle A of the triangle ABC.

10th grade geometry solution4 10th grade geometry solution4


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