SUBJECT: MATHEMATICS TOPIC: TRIANGLES CLASS: X

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1. What value of x will make DE II AB in the given figure? C
X-2 x-1
(x =4)

D E
X x
+2

A
B
2. In figure, DE is parallel to base BC. If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC
A
2.5cm 3.75cm
D E
3.0 cm
(8.25cm)

B C

3. In the figure. XY II BC . Find the length of XY A

E D
PP

B C

5 .D is a point on the side BC of a ∆ABC such that angle ADC = angle BAC. Prove that CA ∕ CD = CB ∕ CA
6. In figure angle ACB = 90• , CD perpendicular to AB, prove that CD2 = BD . CD
C

A D B
7. A vertical pole which is 2.25m long casts a 6.75m long shadow on the ground. At the same time a vertical
Tower casts a 90m long shadow on the ground. Find the height of the tower (30m)
8. If Δ ABC ~ Δ PQR. Also ar (ΔABC) = 4 ar (Δ PQR). If BC = 12cm, find QR (6cm)
9. The areas two similar triangles ABC and DEF are 36 cm2 and 81 cm2 respectively. If EF = 6.9 cm,
determine BC
(4.6 cm)
10. Two isosceles triangles have equal angles and their areas are in the ratio 81: 25. Find the ratio of their
Corresponding heights
11. D, E and F are respectively the mid points of the sides BC, CA and AB of ΔABC. Find the ratio of the areas
of Δ DEF and Δ ABC
(1 : 4)
12. The perimeters of two similar triangles are 36cm and 48cm respectively. If one side of the first triangle is
9cm, what is the corresponding side of the other triangle (12cm)
13. In triangle ABC, AB= C A BC = 2a. Prove that ∟A = 90˚
= a and
√3a,
14. In triangle ABC, ∟BAC = 90˚ and AD ┴ BC. If BD = 8cm, DC= 18 cm, find AD
15. Two poles of height 8m and 13m stand on a plane ground. If the distance between their tips is 13m, find
the distance between their feet
(12m)
16.Two poles of height 10m and 15m stand vertically on a plane ground. If the distance between their feet is
5√3m, find the distance between their tops (10m)
17. The perpendicular from A on side BC of a triangle ABC intersects BC at D such that BD = 3CD. Prove
that 2 AB2 – 2 AC2 = BC2
18. In an isosceles triangle ABC with AB = AC, BD is a perpendicular from B to the side AC. Prove that
BD2 - CD2 = 2CD . AD

19. P and Q are points on the sides CA and CB respectively of a ΔABC right angled at C. Prove that
AQ2 + BP2 = AB2 + PQ2
20. In ∆2 +ABC,
AC2 If= AD is2the
2(AD + BD 2
) an,show that AB
m edi
21. In figure, T trisects the side QR of right triangle PQR. P
Prove that 8 PT2 = 3 PR2 + 5 PS2

Q S T R

22. If BL and CM are medians of a triangle ABC right angled at A, then prove that 4( BL2 + CM2 ) = 5 BC2
23. In a triangle ABC, AB = BC = CA = 2a and AD perpendicular to BC. Prove that AD= a √3 and area of
2
∆ ABC = √3 a
24. In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3A2 =4 AD2
25. In a triangle ABC, AD is perpendicular on BC , prove that AB2 + CD2 = AC2 + BD2
26. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares on its
diagonals
27. P is a point in the interior of rectangle ABCD. If P is joined to each of the vertices of the rectangle, prove
That PB2 + PD2 = PA2 + PC2