Question

ABC is an isoseles triangle with AB=AC and BD and CE are its two median show that BD=CE​

Answer 1

Step-by-step explanation:

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Answer 2

$\Large{\underline{\underline{\bf{Given:}}}}$

• ABC is an isosceles triangle with AB = AC
• BD and CE are the two medians

$\Large{\underline{\underline{\bf{To\:Prove:}}}}$

• To show that BD = CE

$\Large{\underline{\underline{\bf{Proof:}}}}$

→ Consider ΔBEC and ΔCDB in the figure

• BC = BC (common side)
• Angle B = Angle C (Base angles of an isosceles triangle are equal)
• BE = DC (It is an isosceles triangle and BD and CE are medians)

→ Hence ΔBEC $\cong$ ΔCDB by SAS criteria

→ $\therefore$ BD = CE by CPCT

  $\Large{\bf{Hence\:Proved}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

• The base angles of an isosceles triangle are equal
• The median is a line from the vertex of a triangle to the opposite side and divides it into two halves