ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that
i) ΔABD ≅ ΔACE
ii) AB = AC i.e., ABC is an isosceles triangle.
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ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that
i) ΔABD ≅ ΔACE
ii) AB = AC i.e., ABC is an isosceles triangle.
ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that
i) ΔABD ≅ ΔACE
ii) AB = AC i.e., ABC is an isosceles triangle.
Given that BD ⊥ AC; CE ⊥ AC
BD = CE
Now in ΔABD and ΔACE
∠ADB = ∠AEC (∵ given 90°)
∠A = ∠A (commori angle)
BD = CE
∴ ΔABD = ΔACE (∵ AAS congruence)
⇒ AB = AC (∵ C.P.C.T)