Question

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Answer 1

Answer:

Given ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal

In ΔADB and ΔACE

∠ADB=∠AEC=90

0

(altitudes BD and CE to sides AC and AB)

BD=CE (Given altitudes are equal)

∠BAD=∠DAB (Common angle )

ΔABD≅ΔACE [by SAS congruence]

So AB=AC

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

(i) In ∆ABE and ∆ACE, we have

∠AEB = ∠AFC

[Each 90° as BE ⊥ AC and CF ⊥ AB]

∠A = ∠A [Common]

BE = CF [Given]

∴ ∆ABE ≅ ∆ACF [By AAS congruency]

(ii) Since, ∆ABE ≅ ∆ACF

∴ AB = AC [By C.P.C.T.]

⇒ ABC is an isosceles triangle.

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