1. Two triangles will be similar if their corresponding sides are proportional.
2. Two triangles will be similar if their ____ sides are proportional.
3. If two triangles are equiangular (have equal corresponding angles), then the ratios of their corresponding sides will be equal; that is, their corresponding sides will be proportional.
4. Two triangles will be similar if their sides are ____________ proportional.
5. Two quadrilaterals will be similar if their corresponding angles are ______ [equal / proportional] and corresponding sides are ______ [unequal / proportional].
6. Match the items on the left with those on the right (any two):
7. If the ratio of the areas of two similar triangles is 64:49, then find the ratio of their corresponding sides.
8. If two triangles are similar, prove that their corresponding sides are proportional.
9. Two acute-angled triangles ∆ABC and ∆PQR are similar. Their circumcenters are X and Y respectively. If BC and QR are corresponding (similar) sides, then prove that BX : QY = BC : QR.
10. Two polygons will be similar when their sides are_____ and their angles are _____.
11. The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of a side of the first triangle is 4 cm, then the length of the corresponding side of the second triangle will be ____ .
12. If the ratio of the lengths of two corresponding sides of two similar triangles is 7:11, then their perimeter ratio is _____.
13. “The perimeters of two similar triangles are 24 cm and 16 cm respectively. If one side of the second triangle is 6 cm, what will be the length of the corresponding side of the first triangle.”
14. "Two acute-angled triangles ∆ABC and ∆PQR are similar. Their circumcenters are X and Y respectively. If BC and QR are corresponding sides, then prove that: BX : QY = BC : QR."
15. If the lengths of the sides of two triangles are in proportion, then the triangles will be ——.
16. If two cones have equal base radii and their heights are in the ratio 2:3, then the ratio of their volumes will be ______.
17. \(\triangle\)ABC ~ \(\triangle\)DEF; BC and EF are corresponding sides. If BE : EF = 1 : 3, then the ratio of the areas of \(\triangle\)ABC and \(\triangle\)DEF will be 1 : 27.
18. If the ratio of the lengths of two corresponding sides of two similar triangles is 7:11, then the ratio of their perimeters is —
(a) 11:7 (b) 49:121 (c) 7:11 (d) 121:49
19. The corresponding sides of two similar-angled triangles are ________.
20. If two similar triangles have equal areas, then they will be congruent.
21. If the ratio of the volumes of two cubes is 1:27, then the ratio of their total surface areas will be _____.
22. If Raima invests 600 rupees for 5 months and Susmita invests 500 rupees for 9 months in a business, their profit share ratio will be ______.
23. Prove that the perimeters of two similar triangles are proportional to their corresponding sides.
24. The corresponding sides of two similar triangles are _____.
