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प्रश्न
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
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उत्तर
If altitudes CE and BF of a triangle ABC are equal, then
AB A C
Reason: From RHS congruence criterionΔ BEC ≅CFB ⇒∠EBC = ∠FCB⇒∠ABC = ∠ACB⇒ AC=AB
[ ∵Sides opposite to equal angels are equal]
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संबंधित प्रश्न
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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ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
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[Hint: Recall how ∠B = ∠C is proved when AB = AC].
