Mathematics

If BM = DM then AM = CM :

If BM = DM then AM = CM: Triangles, Concise Mathematics Solutions ICSE Class 9.
  1. yes

  2. no

  3. can't say

  4. none of these

Triangles

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Answer

Given, BM = DM

⇒ M bisects line BD.

AB is parallel to CD.

In ΔABM and ΔCDM,

⇒ BM = DM

⇒ ∠MBA = ∠MDC (Alternate angles are equal)

⇒ ∠MAB = ∠MCD (Alternate angles are equal)

∴ ΔABM ≅ ΔCDM (By AAS congruency criterion)

By C.P.C.T.

⇒ AM = CM

Hence, option 1 is the correct option.

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