Q14 of 95 Page 5

In the adjoining figure, AD is the bisector of ∠BAC. If AB = 10 cm, AC = 6 cm, BC = 12 cm, find BD.

Given: AD is the bisector of BAC


and by Angle-Bisector theorem which states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.











And BC – CD = DB


⇒ 12 – 4.5 = DB


⇒ DB = 7.5cm


More from this chapter

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12

P and Q are points on sides AB and AC respectively of Δ ABC. For each of the following cases, state whether PQ || BC.

(i) AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm.


(ii) AB= 1.28 cm, AC = 2.56 cm, AP= 0.16 cm and AQ = 0.32 cm


(iii) AB = 5 cm, AC =10 cm, AP= 4 cm, AQ = 8 cm.


(iv) AP= 4 cm, PB= 4.5 cm, AQ = 4 cm, QC = 5 cm.

 13

In the adjoining figure, AD is the bisector of ∠BAC. If BC = 10 cm, BD = 6 cm AC = 6 cm, then find AB.

 15

In EABC, AD is the bisector of ∠A. If AB = 3.5 cm, AC = 4.2 cm, DC = 2.4 cm. Find BD.

 1

State which of the following pairs of triangles are similar. Write the similarity criterion used and write the pairs of similar triangles in symbolic form (all lengths of sides are in cm).

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)