Q. 1. State which pairs of triangles in the figures are similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form.; Q. 2. In the figure, triangle ODC is similar to triangle OBA, angle BOC = 125 degree and angle CDO = 70 degree. Find angle DOC, angle DCO and angle OAB.; Q. 3. Diagonals AC and BD of a trapezium ABCD with AB parallel to DC intersect each other at the point O. Using a similarity criterion for two triangles, show that OA/OC=OB/OD.; Q. 4. In the figure, QR/QS=QT/PR and angle 1 = angle 2. Show that triangle PQS is similar to the triangle TQR.; Q. 5. S and T are points on sides PR and QR of a triangle PQR such that angle P=angle RTS. Show that the triangle RPQ is similar to the triangle RTS.; Q. 6. In the figure, if triangle ABE is congruent to the triangle ACD, show that the triangle ADE is similar to the triangle ABC.; Q. 7. In the figure, altitudes AD and CE of the triangle ABC intersect each other at a point P. Show that: (i) Triangle AEP is similar to triangle CDP, (ii) Triangle ABD is similar to triangle CBE, (iii) Triangle AEP is similar to triangle ADB, (iv) Triangle PDC is similar to triangle BEC; Q. 8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that the triangle ABE is similar to the triangle CFB.; Q. 9. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that: (i) Triangle ABC is similar to the triangle AMP, (ii) CA/PA=BC/MP,; Q. 10. CD and GH are respectively the bisectors of angle ACB and the angle EGF such that D and H lie on sides AB and FE of the triangle ABC and the triangle EFG respectively. If the triangle ABC is similar to the triangle FEG, show that: (i) CD/GH=AC/FG, (ii) Triangle DCB is similar to the triangle HE, (iii) Triangle DCA is similar to the triangle HGF,; Q. 11. In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If AD is perpendicular to BC and EF is perpendicular to AC, prove that triangle ABD is similar to the triangle ECF.; Q. 12. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of the triangle PQR. Show that triangle ABC is similar to the triangle PQR.; Q. 13. D is a point on side BC of a triangle ABC such that the angle ADC is equal to the angle BAC. Show CA^2=CB×CD.; Q. 14. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that the triangle ABC is similar to the triangle PQR.; Q. 15. A vertical pole of length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28m long. Find the height of the tower.; Q. 16. If AD and PM are medians of triangles ABC and PQR respectively where the triangle ABC is similar to the triangle PQR, prove that AB/PQ=AD/PM.
