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Triangles on the Same Base and between the Same Parallels

Question 3 AB...

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Question 3
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

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Solution

$I n Δ A E B a n d Δ A F C ∠ A E B = ∠ A F C (e a c h 90^{\circ}) ∠ A = ∠ A (c o m m o n a n g l e) A B = A C (g i v e n) ∴ Δ A E B ≅ Δ A F C (b y A A S c o n g r u e n c e r u l e) \Rightarrow B E = C F (b y C . P . C . T)$

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Triangles on the Same Base and between the Same Parallels

Standard IX Mathematics

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