theorem : the sides opposite to equal angles of a triangle are equal prove this class 9

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theorem : the sides opposite to equal angles of a triangle are equal prove this class 9

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Kennedy 1 month 2021-08-23T00:19:18+00:00 1 Answer 0 views 0

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    2021-08-23T00:20:32+00:00

    Answer:

    Step-by-step explanation:

    Given: In ∆ABC, ∠XYZ = ∠XZY.

    To prove: XY = XZ

    Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.

    Proof:

             Statement                                             Reason

    1. In ∆XYM and ∆XZM,                         1.

    (i) ∠XYM = XZM                                      (i) Given                          

    (ii) ∠YXM = ∠ZXM                                  (ii) XM bisects ∠YXZ

    (iii) XM = XM                                           (iii) Common side

    2. ∆XYM ≅ ∆XZM                                  2. By AAS criterion.

    3. XY = XZ. (Proved)                                3. CPCTC.

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