Q8 of 168 Page 4

If D and E are points on sides AB and AC respectively of a such that and BD = CE. Prove that is isosceles.

We have DE∥BC


by the converse of proportionality theorem


AD/DB=AE/EC


AD/DB=AE/DB [BD=CE]


AD=AE


Adding D both sides


AD+BD=AE+DB


AD+BD=AE+EC [BD=CE]


AB=AC


⊿ABC is isosceles


More from this chapter

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6

M and N are points on the sides PQ and PR respectively of a . For each of the following cases, state whether :

(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm


(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

 7

In three line segments OA, OB, and OC, points L, M, N respectively are so chosen that and but neither of L, M, N nor of A, B, C are collinear. Show that .

 1

In a , AD is the bisector of , meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AV = 4.2 cm, find DC.


(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.


(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.


(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.


(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.


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


(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.


(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

 2

In Fig. 4.57, AE is the bisector of the exterior meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, find CE.