Q11 of 95 Page 5

If D and E are points on sides AB and AC respectively of ΔABC and AB = 12 cm, AD = 8 cm, AE = 12 cm, AC =18 cm, then prove that DE || BC.


Given: AB = 12cm, AD =8cm, AE = 12cm and AC = 18cm


To Prove: DE || BC


In ABC,





Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.


Hence, DE || BC [by converse of basic proportionality theorem]


Hence, Proved.


More from this chapter

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9

In the adjoining figure, P and Q are points on sides AB and AC respectively of mix such that PQ || BC and AP= 8 cm, AB =12 cm, AQ = 3x cm, QC = (x + 2) cm. Find x.

 10

In the adjoining figure, DE || BC, find x.

 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.