Pythagoras Theorem and its Applications

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  • Q1

    In the given figure, the value x is

    Marks:1
    Answer:

    10

    Explanation:

    In the given figure of right-angled triangle, we have

    YZ2 = YX2 + XZ2 [By Pythagoras theorem]
    x2 = 62 + 82
    x = 36 + 64 = 100
    x = 10

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  • Q2

    In right angled triangle PQR, which of the following is true?

    Marks:1
    Answer:

    m2 = l2 + n2

    Explanation:

    According to the Pythagoras theorem, we have
    (Hypotenuse)2 = (Altitude)2 + (Base)2

    Therefore, the property, which holds true for given right angled triangle, will be
    m2 = l2 + n2

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  • Q3

    In a right angled triangle, the hypotenuse is

    Marks:1
    Answer:

    the longest side.

    Explanation:

    Since, opposite side of greater angle is greater in a triangle. Since hypotenuse is opposite side of right angle in triangle so it is the longest side.

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  • Q4

    ABC is a right angled triangle in which A = 90° and
    AB = AC. Find B and C.

    Marks:1
    Answer:

    45°, 45°

    Explanation:

    In ABC, A = 90° and AB = AC Then B = C

    According to angle sum property,
    A + B + C = 180°

    90° + B + C = 180°
    90° + 2 B = 180°
    2 B = 180° - 90°
    = 90°
    B = C = 45°

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  • Q5

    In a right angled isosceles triangle shown below, what is the value of angle ACO.

    Marks:1
    Answer:

    135o

    Explanation:

    Since, it is an Isosceles right angle triangle, so the values of angles other than 90o are 45o each. And angle ACO and angle ACB are forming a linear pair, which means their sum will be 180o and hence the value of angle ACO is 135o.

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