Triangles Class 10 Extra Questions

Triangles Class 10 Extra Questions

CHAPTER- 6 TRIANGLES

Multiple Choice Questions (Triangles Class 10 Extra Questions)

1. If ∆ABC ~ ∆PQR, perimeter of ∆ABC = 32 cm, perimeter of ∆PQR = 48 cm and PR = 6 cm, then , the length of AC is

a)2cm           b) 4cm           c) 8cm          d) 6cm
2. ∆ABC ~ ∆DEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm and DF = 7.5 cm, then the perimeter of ∆DEF is
a) 30cm           b) 40cm           c) 80cm          d) 60cm
3. If ∆ABC ~ ∆RPQ, AB = 3 cm, BC = 5 cm, AC = 6 cm, RP = 6 cm and PQ = 10, then  QR is
a) 15cm           b) 4cm           c) 12cm          d) 18cm
4. In ∆DEW, AB || EW. If AD = 4 cm, DE = 12 cm and DW = 24 cm, then find the value of DB
a)2cm           b) 4cm           c) 8cm          d) 6cm
5. If ∆ABC ~ ∆DEF ,such that 2AB=DE and BC=8cm then EF=
a)16cm           b) 12cm           c) 8cm          d) 4cm
6. XY || BC of ∆ABC cutting AB at X and AC at Y.If AB=4BX and YC =2cm then AY=
a)2cm            b) 4cm              c) 8cm             d) 6cm
7. If ABC and DEF are similar triangles such that angles A and E are 47⁰  and  83⁰ respectively. Then angle B is…
a)35⁰           b) 50⁰                   c) 75⁰                   d) 83⁰
8. The lengths of the diagonals of a rhombus are 32 cm and 24 cm. What is the perimeter of the rhombus.
a)20cm           b) 40cm           c) 80cm          d) 60cm

Subjective Type Questions (Triangles Class 10 Extra Questions)

9. In ∆ABC, DE || BC, find the value of x. 

10. In the given figure, if DE || BC, AE = 8 cm, EC = 2 cm and BC = 6 cm, then find DE.

11. In the given figure, XY || QR, PQ/XQ=7/3 and PR = 6.3 cm, find YR.

12. In the figure, EF || AC, BC = 10 cm, AB = 13 cm and EC = 2 cm, find AF.

13. X and Y are points on the sides AB and AC respectively of a triangle ABC such that AX/AB=1/4, AY = 2 cm and YC = 6 cm. Find whether XY || BC or not.

14. In the given figure, ∠A = 90°, AD ⊥ BC. If BD = 2 cm and CD = 8 cm, find AD.

15. In the figure ABC and DBC are two right triangles. Prove that AP × PC = BP × PD.

16. If a line segment intersects sides AB and AC of a ∆ABC at D and E respectively and is parallel to BC, prove that AD/AB=AE/AC.
17. ∆ABC ~ ∆PQR. AD is the median to BC and PM is the median to QR. Prove that AB/PQ=AD/PM.
18. Two triangles ABC and DBC are on the same base BC and on the same side of BC in which angle A and D are 90⁰ each. If CA and BD meet each other at E, then show that AE.EC = BE.ED
19. Assertion (A): If ∆ABC and ∆PQR are congruent triangles, then they are also similar triangles.
Reason (R): All congruent triangles are similar but the similar triangles need not be congruent.
20. Assertion (A): In the ∆ABC, AB = 24 cm, BC = 10 cm and AC = 26 cm, then ∆ABC is a right angle triangle.
Reason (R): If in two triangles, their corresponding angles are equal, then the triangles are similar

1. CASE STUDY:

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house is 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.
(i). What is the height of the tower? 
(ii).What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?
(iii). What is the height of Ajay’s house?
(iv)When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?

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