Q1: Which of the following triangles have the same side lengths?
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) None of these
Q2: Area of an equilateral triangle with side length a is equal to:
(a) (√3/2)a
(b) (√3/2)a^{2}
(c) (√3/4) a^{2}
(d) (√3/4) a
Q3: D and E are the midpoints of side AB and AC of a triangle ABC, respectively, and BC = 6 cm. If DE  BC, then the length (in cm) of DE is:
(a) 2.5
(b) 3
(c) 5
(d) 6
Q4: The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of the rhombus in length is:
(a) 20 cm
(b) 8 cm
(c) 10 cm
(d) 9 cm
Q5: Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 sq.cm, then the area of the large triangle is:
(a) 230 sq.cm.
(b) 106 sq.cm
(c) 107 sq.cm.
(d) 108 sq.cm
Q6: If the perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of the third side will be:
(a) 30 cm
(b) 40 cm
(c) 50 cm
(d) 60 cm
Q7: If triangles ABC and DEF are similar and AB = 4 cm, DE = 6 cm, EF = 9 cm, and FD = 12 cm, the perimeter of triangle ABC is:
(a) 22 cm
(b) 20 cm
(c) 21 cm
(d) 18 cm
Q8: The height of an equilateral triangle of side 5 cm is:
(a) 4.33 cm
(b) 3.9 cm
(c) 5 cm
(d) 4 cm
Q9: If ABC and DEF are two triangles and AB/DE = BC/FD, then the two triangles are similar if
(a) ∠A = ∠F
(b) ∠B = ∠D
(c) ∠A = ∠D
(d) ∠B = ∠E
Q10: Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
(a) 2: 3
(b) 4: 9
(c) 81: 16
(d) 16: 81
Q1: The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.
Q2: Determine whether the triangle having sides (b − 1) cm, 2√b cm and (b + 1) cm is a right angled triangle.
Q3: Sides of triangles are given below. Determine which of them are right triangles.In case of a right triangle, write the length of its hypotenuse.
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm,4 cm,5 cm
(iii) 40 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
Q4: In ΔABC, AD is perpendicular to BC. Prove that:
a. AB^{2} + CD^{2} = AC^{2} + BD^{2}
b. AB^{2} − BD^{2} = AC^{2} − CD^{2}
Q5: Triangle ABC is right angled at B and D is the mid  point of BC.
Prove that: AC^{2 }= 4AD^{2} − 3AB^{2}
Q6: ABC is an isosceles triangle, right angled at C. Prove that AB^{2} = 2BC^{2} .
Q7: A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Q8: The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?
Q9: The areas of two similar triangles are 121 cm^{2} and 64 cm^{2} respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.
Q10: DEF is an equilateral triangle of side 2b. Find each of its altitudes.
116 videos420 docs77 tests

1. What are the different types of triangles? 
2. How do you find the area of a triangle? 
3. Can a triangle have two right angles? 
4. How can you determine if three given side lengths form a triangle? 
5. What is the Pythagorean theorem and how is it used in triangles? 

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