Important Questions of Triangles Mathematics | Zigya
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    Mathematics : Triangles

    Multiple Choice QuestionsShort Answer Type

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    211. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. 
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    212. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
    (A) 2 : 1   (B) 1 : 2  (C) 4 : 1   (D) 1 : 4.
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    213.

    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.

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    Multiple Choice QuestionsLong Answer Type

    214. Sides of some triangles are given below. Determine which of them are right triangles. In case of a right angle, write the length of its hypotenuse.
    (i) 7 cm, 24 cm, 25 cm
    (ii) 3 cm, 8 cm, 6 cm
    (iii) 50 cm, 80 cm, 100 cm
    (iv) 13 cm, 12 cm, 5 cm.
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    215. PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR show that PM2 = QM × MR.
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    216.

    In the given fig, ABD is a triangle right angled at A and AC ⊥ BD. Show that
    (i) AB2 = BC .BD
    (ii) AC2 = BC. DC
    (iii) AD2 = BD . CD

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    Multiple Choice QuestionsShort Answer Type

    217. ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.
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    218. ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ∆ABC is a right triangle.
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    Multiple Choice QuestionsLong Answer Type

    219. ABC is an equilateral triangle of side 2a. Find each of its altitudes.
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    220. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
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