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Class 10 Mathematics: Triangles
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MCQs on triangles similar figures, triangle similarity criteria, similar triangle area and pythagoras theorem.

Class 10 Mathematics: Triangles
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25 Questions

1. ∆ABC ∼ ∆PQR, AD & PS are the angle bisectors of respectively. If AD = 1.5cm and PS = 2.3 cm then, what will be the ratio of the areas of ∆ABC and ∆PQR?
2. What will be the length of the square inscribed in a circle of radius 5 cm?
3. If DE∥BC, AD = 4cm, BD = 7.5cm, AE = 6.4 cm & DE = 5cm then what will be the lengths of AC and BC?
4. If ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R then, ∆ABC & ∆PQR are similar according to which test?
5. What is the value of x?
6. What will be the length of the altitude of an equilateral triangle whose side is 9 cm?
7. If \(\frac {AB}{XY} = \frac {BC}{YZ} = \frac {AC}{XZ}\) then, ∆ABC & ∆XYZ are similar according to which test?
8. In two similar triangles ∆ABC and ∆DEF, AB = 15cm, DE = 5cm. If AL and DM are the altitudes of the triangles ABC, DEF respectively, then what will be the ratio of their altitudes?
9. The area of two similar triangles is 25cm2 and 121cm2. If the median of the bigger triangle is 10 cm, then what will be the corresponding median of the smaller triangle?
10. In ∆PQR, PS is the bisector of ∠P. If PQ = 6.4cm, PR = 14cm, QS = 6cm. What will be the length of PS and QR?
11. The heights of two vertical lamp posts are 33 m and 24 m high. If the distance between them is 40 m, then what will be the distance between their tops?
12. What will be the distance of the foot of ladder from the building, if the ladder of 12 m high reaches the top of a building 35 m high from the ground?
13. The perimeters of two similar triangles ABC, PQR is 64 cm and 24 cm respectively. If PQ is 12 cm what will be the length of AB?
14. If the side of rhombus is 13 cm and one of its diagonals is 24 cm, then what will be length of the other diagonal?
15. The figure shown is congruent.

16. ∆ABC is a right-angled triangle, right angled at B and BD ⊥ AC. If BD = 10cm, AB = 5 cm and BC = 5 cm then AC will be?
17. The figure shown is similar.

18. A man travels A to B, B to C, C to D and then finally D to E. What will be the shortest route the man could have taken?
19. The lengths of diagonals of a rhombus are 10 cm and 8 cm. What will be the length of the sides of rhombus?
20. In the given figure, LM∥PQ, what will be the relation between x, a, b and c?
21. In the given figure PQ∥BC, and 3AP=4PB. What will be the ratio of areas ∆ABC and trap.(PQCB)?
22. In the given figure, AC is the angle bisector and AB = 5.2 cm, AD = 4.5 cm. What will be ratios of areas of ∆ABC and ∆ACD?
23. What will be the ratios of areas of similar ∆ABC and ∆PQR, if the altitudes of the triangles are 10cm and 5.5cm respectively?
24. In the given figure DE∥BC, if AD = 5.9cm, DB = 4cm and AE = 7cm then, what will be the value of AC?
25. Two geometric figures which have same shape and size are known as congruent.

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