1. The corresponding sides of two similar triangles are _____.
2. If the ratio of the areas of two similar triangles is 64:49, then find the ratio of their corresponding sides.
3. If the ratio of the lengths of two corresponding sides of two similar triangles is 7:11, then their perimeter ratio is _____.
4. Two triangles will be similar if their corresponding sides are _____.
5. Prove that the perimeters of two similar triangles are proportional to their corresponding sides.
6. Match the items on the left with those on the right (any two):
7. If two triangles are similar, prove that their corresponding sides are proportional.
8. 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.
9. 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
10. 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 ____ .
11. The perimeters of two similar triangles are 20 cm and 16 cm respectively. If one side of the first triangle is 9 cm, what is the length of the corresponding side of the second triangle?
12. “The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of one side of the first triangle is 9 cm, what is the length of the corresponding side of the second triangle.”
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 triangles will be similar if their corresponding sides are proportional.
15. 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.
16. “The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of one side of the first triangle is 9 cm, calculate the length of the corresponding side of the second triangle.”
17. "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."
18. The corresponding sides of any two similar polygonal figures are proportional.
19. The lengths of the sides of two similar triangles are always equal.
20. The perimeters of two similar triangles are 27 cm and 16 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.
21. ABC and POR are two similar triangles. If BC = 5 cm, QR = 4 cm, and the height AD = 3 cm, then what is the length of the height PE?
(a) 4.2 cm (b) 1.25 cm (c) 5.4 cm (d) 2.4 cm
22. Prove that if a perpendicular is drawn from the right angle vertex of a right-angled triangle to the hypotenuse, then the two adjacent triangles formed are similar to each other and each is also similar to the original triangle.
23. If the lengths of the sides of two triangles are in proportion, then the triangles will be ——.
24. If a perpendicular is drawn from the right angle vertex of a right-angled triangle to the hypotenuse, then the two triangles formed on either side of that perpendicular are similar to each other. — Prove it.
25. Two polygons will be similar when their sides are_____ and their angles are _____.
26. If the corresponding angles of two quadrilaterals are equal, then the two quadrilaterals are similar.
27. Two triangles will be similar if their ____ sides are proportional.
28. Prove that if a perpendicular is drawn from the right angle vertex of a right-angled triangle to the hypotenuse, the two triangles formed are similar to each other.
29. If the corresponding angles of two quadrilaterals are equal, then the two quadrilaterals are similar.
30. Prove that if a perpendicular is drawn from the right-angle vertex of a right-angled triangle to the hypotenuse, then the two triangles formed on either side of the perpendicular are similar to each other.
