Q2 of 168 Page 4

In a, D and E are points on the sides AB and AC respectively. For each of the following cases show that :

(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.


(ii) AB = 5.6 cm, AD = 1.4 cm, AE = 7.2 cm and AC = 1.8 cm.


(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.


(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.


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(i) AB = 12 cm, AD = 8 cm, and AC = 18 cm.


∴ DB=AB-AD


= 12-8


=4 cm


EC=AC-AE


= 18-12


= 6 cm


Now AD/DB=8/4=2


AE/EC=12/6=2


Thus DE divides side AB and AC of ⊿ ABC in same ratio


Then by the converse of basic proportionality theorem.


(ii)



AB = 5.6 cm, AD = 1.4 cm, AE = 1.8 cm and AC = 7.2 cm


∴ DB=AB-AD


DB=5.6-1.4


DB= 4.2 cm


And EC=AC-AE


EC= 7.2-1.8


EC=5.4


Now AD/DB=1.4/4.2=1/3


AE/EC=1.8/5.4=1/3


Thus DE divides side AB and AC of ⊿ ABC in same ratio


Then by the converse of basic proportionality theorem.


(iii)



we have


AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm


∴ AD=AB-DB


AD=10.8-4.5


AD= 6.3 cm


And EC=AC-AE


EC= 4.8-2.8


EC=2 cm


Now AD/DB=6.3/4.5=7/5


AE/EC=2.8/2=28/20=7/5


Thus DE divides side AB and AC of ⊿ ABC in same ratio


Then by the converse of basic proportionality theorem.


(iv)



DE∥BC


We have,


AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm


Now AD/DB=5.7/9.5=57/95 =3/5


AE/EC=3.3/5.5=33/55=3/5


Thus DE divides side AB and AC of ⊿ ABC in same ratio


Then by the converse of basic proportionality theorem.


More from this chapter

All 168 →
2

Write the truth value (T/F) of each of the following statements:

(i) Any two similar figures are congruent.


(ii) Any two congruent figures are similar.


(iii) Two polygons are similar, if their corresponding sides are proportional.


(iv) Two polygons are similar if their corresponding angles are proportional.


(v) Two triangles are similar if their corresponding sides are proportional.


(vi) Two triangles are similar if their corresponding angles are proportional.

 1

In a , D and E are points on the sides AB and AC respectively such that

(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.


(ii) If and AC = 15 cm, find AE.


(iii) If and AC = 18 cm, find AE.


(iv) If AD = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x.


(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.


(vi) If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC.


(vii) If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.


(viii) If and EC = 2.5 cm, find AE.


(ix) If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value of x.


(x) If AD = 8x - 7, DB = 5x – 3, AE = 4x - 3 and EC = (3x – 1), find the value of x.


(xi) If AD = 4x – 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x - 3, find the volume x.


(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.

 3

In a, P and Q are points on sides AB and AC respectively, such that . If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ.

 4

In a ΔABC, D and E are points on AB and AC respectively such that DE||BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.