Q3 of 56 Page 134

Two triangles ABC and DBC are formed on the same base BC. If AD and BC intersect each other at O then prove that




…(1)


In ΔAOF & ΔDOG,


∠AOF = ∠DOG |vertically opp. angles


∠AFO = ∠DGO |both right angles


ΔAOF~ΔDOF by AA Similarity Rule


…(2)


From (1) & (2),



Hence, proved.


More from this chapter

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1

Answer the following in True or False. Write the reason of your answer (if possible).

(i) The ratio of the corresponding sides of two similar triangles is 4 : 9. Then the ratio of the areas of these triangles is 4 : 9.


(ii) In two triangles respectively ΔABC and ΔDEF of then ΔABC ≅ ΔDEF.


(iii) The ratio of the areas of two similar triangles in proportional to the squares of their sides.


(iv) If ΔABC and ΔAXY are similar and the values of their areas are the same then XY and BC may be coincident sides.

 2

If ΔABC~ΔDEF and their areas are respectively 64 sq cm and 121 sq cm. If EF = 15.4 cm then find BC.

 4

Find the solutions of the following questions:

In ΔABC DE || BC and AD : DB = 2 : 3 then find the ratio of the areas of ΔADE and ΔABC.

 4

Find the solutions of the following questions:

PB and QA are perpendicular at points B and A of line segment AB. If P and Q lie on opposite sides of AB and on joining P and Q it intersects AB at O and PO = 5 cm, QO = 7 cm, area of ΔPOB = 150 cm2 then find the area of ΔQOA.