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Show that the relation R defined in the set A of all triangles as `R={(T _(1), T _(2))):T _(1)` is similar to `T _(2)`} is equivalence relation. Consider three right angle triangles `T_(1)` with sides `3,4,5,T_(2)` with sides `5,12,13 and T_(3)` with sides `6,8,10.` Which triangles among ` T_(1), T_(2) and T_(3)` are related ?

Answer

Step by step text solution for Show that the relation R defined in the set A of all triangles as R={(T _(1), T _(2))):T _(1) is similar to T _(2)} is equivalence relation. Consider three right angle triangles T_(1) with sides 3,4,5,T_(2) with sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles among T_(1), T_(2) and T_(3) are related ? by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Show that the relation R defined in the set A of all polygons as R = {(P _(1), P _(2)): P _(1) and P _(2) have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

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Knowledge Check

  • If (t, 2t), (-2, 6), and (3, 1) are collinear, t =

    A
    `3//4`
    B
    `4//3`
    C
    `5//3`
    D
    `3//5`

  • The tangents at the points (a t_(1)^(2), 2 a t_(1)), (a t_(2)^(2), 2 a t_(2)) are right angles if

    A
    `t_(1) cdot t_(2)=-1`
    B
    `t_(1) cdot t_(2)=1`
    C
    `t_(1) cdot t_(2)=2`
    D
    `t_(1) cdot t_(2)=-2`

  • A Carnot engine operating between temperatures T_(1) and T_(2) has efficiency (1)/(6) . When T_(2) is lowered by 62 K its efficiency increase to (1)/(3) . Then T_(1) and T_(2) are, resectively :

    A
    372 K and 330 K
    B
    330 K and 268 K
    C
    310 K and 248 K
    D
    372 K and 310 K

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    Show that efficiency of Caront's ideal heat engine is eta=(1-(T_(2))/(T_(1))) .

    In the following graph, say whether T_(1) gt T_(2) or not.

    Find the matrices of transformation T_(1)T_(2) and T_(2)T_(1) when T_(1) is rotated through an angle 60^(@) and T_(2) is the reflection in the Y-asix Also, verify that T_(1)T_(2)!=T_(2)T_(1).

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