Question

Prove that the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal

Answer 1

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Answer 2

Answer:

The answer is proved below.

Step-by-step explanation:

Suppose we have an isosceles triangle ABC where AB = AC, Then automatically ∠ABC = ∠ACB

Suppose we draw perpendiculars from B to AC intersecting at a point D and C to AB intersecting at a point E. We need to prove that BE = CD

In Triangle ABE and triangle ACD

∠AEB = ∠ADC (Perpendicular drawn hence 90 )

∠EAB = ∠DAC (Common Angle)

AB = AC (Equal side of the isosceles triangles)

Hence Proved ABE ≈ ACD

BE = CD (CPCT)

Hence Proved

What are isosceles triangles

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