Pove that the sum of any two side of a triangle is greater than twice the median drow to the third side.it​

Question

Pove that the sum of any two side of a
triangle is greater than twice the median
drow to the third side.it​

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Brielle 1 month 2021-08-14T15:04:20+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-14T15:05:55+00:00

    Step-by-step explanation:

    Given : Triangle ABC in which AD is the median.

    To prove:AB+AC>2AD Construction :

    Extend AD to E such that AD=DE. Now join EC.

    Proof:

    In AADB and AEDC AD=DE[ By construction]

    D is the midpoint BC.[DB=DB]

    AADB=AEDC [vertically opposite angles]

    Therefore A ADB = AEDC [ By SAS congruence criterion.]

    –> AB=ED[Corresponding parts of congruent triangles ]

    In ΔΑEC , AC+ED> AE [sum of any two sides of a triangle is greater than the third side] AC+AB>2AD[AE=AD+DE=AD+AD=2AD

    and ED=AB]

    Hence proved

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