Triangles-Sample Papers

1.  Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? (2 marks)

2.  ΔABC~ΔPQR with BC/QR = 1/3, then find ar(ΔPQR)/ar(ΔABC). (2 marks)

3.  Is the triangle with sides 14cm, 12cm and 17cm a right triangle? Why? (1 mark)

4.  The lengths of diagonals of a rhombus are 24 cm and 32 cm. Find the length of its sides. (2 marks)

5.  PQR is an isosceles triangle with QP=QR. If PR²= 2QR², prove that ΔPQR is rightangled. (2 marks)

6.  In a triangle ABC, line DE is drawn parallel to side BC such that AD/DB = AE/EC. Show that BAC is an isosceles triangle. (3 marks)

7.  A 20 m long vertical pole casts a shadow 10 m long on the ground. At the same time a tower casts a shadow 50 m long on the ground. Find the height of the tower. (2 marks)

8.  State and prove basic proportionality theorem. (4 marks)

9.  L and M are two points on the sides DE and DF of the triangle DEF such that DL=4, LE=4/3, DM=6 and DF=8. Is LM parallel to EF? Why? (1 mark)

10.  In a triangle PQR and MST, ∟P=55°, ∟Q = 25°, ∟M = 100° and ∟S = 25°. Is ΔQPR similar to ΔTSM? Why? (1 mark)