Maths-
General
Easy

Question

In straight triangle ABC, DA = DB = DC. Show that straight angle ACB equals 90 to the power of ring operator.

hintHint:

Using Angles opposite to the equal sides are equal . find the angles and Add using Sum of angles in triangle ABC ,Find ∠ACB = 90°

The correct answer is: ∠ ACB = 90°


    Step 1:- Find relation between ∠ACD,∠BAC,∠ABC and ∠DCB
    In Δ ACD,

    As DA = DC

    ∠ ACD  =  ∠ BAC(Angles opposite to the equal sides are equal)

    In Δ BCD,

    As DB = DC

    ∠BCD = ∠ABC(Angles opposite to the equal sides are equal)
    In straight capital delta ABC ,

    ∠ BAC + ∠ ABC +  ∠ ACB = 180°(sum of angles in the triangle)

    Substitute ∠ ACD = ∠ BAC and ∠ BCD = ∠ ABC

    ∠ACD + ∠ BCD + ∠ ACB = 180°

    From diagram, we get ∠ ACD  + ∠BCD  = ∠ ACB

    2 × ∠ ACB = 180°  ∠ACB = 90°

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