traingle ABC, if 2 C > 2 B, then, BC> AC AB> AC (c) AB

Question

traingle ABC, if 2 C > 2 B, then,
BC> AC
AB> AC
(c) AB<AC
(d) BC<AC​

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Alice 1 month 2021-08-12T14:48:02+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-12T14:49:49+00:00

    Answer:

    Step-by-step explanation:

    GIVEN: Triangle ABC, <B = x, <A = 2x


    TO PROVE THAT: BC² = AC² + AB * AC


    CONSTRUCTION: CX perpendicular to AB.


    & construct CD = CA ……….. (1)


    PROOF: <A = <D = 2x


    & in triangle CDB, exterior angle 2x = < B+<C


    => < B = < BCD = x


    => CD = DB ( Sides opposite to equal angles of a triangle) ……….. (2)


    Hence, AC = DB …….. (3) By (1) & (2) ………(3)●


    Now, by Extension of Pythagoras theorem for acute triangle…


    BC² = AC² + AB² – 2AB * AX


    => BC² = AC² + AB ( AB – 2AX)


    => BC² = AC² + AB * ( AB – AD) ( since AX = XD)


    => BC² = AC² + AB * DB


    But DB = AC ( by eq (3) )


    Hence, BC² = AC² + AB * AC


    [ Hence Proved]

    hope it helps

    🙂

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