Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Triangles (25 marks, 55 mins)
1. What value of x will make DE || AB in the given figure?
AD = 8x+9, CD = x+3, BE = 3x+4, CE = x (2 marks)
2. A vertical pole which is 2.25 m long casts a shadow 6.75 m long. At the same time, a vertical tower
casts a 90 m long shadow on the ground. Find the height of the tower. (2 marks)
3. Two isosceles triangles have equal angles and their areas are in the ratio 81:25. Find the ratio of their
corresponding heights. (2 marks)
4. The perimeters of two similar triangles are 36cm and 48 cm respectively. If one side of the first triangle
is 9 cm, what is the corresponding side of the other triangle. (2 marks)
5. If BL and CM are medians of a triangle ABC right angled at A, the prove that 4(BL
2
+ CM
2
) = 5 BC
2
(4 marks)
6. Prove that sum of the squares of the sides of the rhombus is equal to the sum of squares of its
diagonals. (3 marks)
7. State and prove Basic Proportionality Theorem. (4 marks)
8. In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3AB
2
= 4AD
2
(3 marks)
9. D is a point on the side BC of a triangle ABC such that ADC = BAC. Prove that CA/CD = CB/CA. (2 marks)
Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1. x = 2
2. 30m
3. 9:5
4. 12 cm
