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प्रश्न
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
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उत्तर
Given that, in two right triangles one side and acute angle of one are equal to the corresponding side and angle of the other
We have to prove that the triangles are congruent
Let us consider two right triangles such that
∠B=∠E=90° .................(1)
AB=DE ..................(2)
∠C=∠F ..................(3)
Now observe the two triangles ABC and DEF
∠C=∠F [From (3)]
∠B=∠E [From (4)]
and AB =DE [From (2)]
So, by AAS congruence criterion, we have
ΔABC≅ΔDEF
∴ The two triangles are congruent
Hence proved
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संबंधित प्रश्न
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If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
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Fill the blank in the following so that the following statement is true.
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Fill the blank in the following so that the following statement is true.
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Fill in the blank to make the following statement true.
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In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.
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CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
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)
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