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Question
In the given figure, △ABC is an isosceles triangle in which AB =
AC and a circle passing through B and C intersects AB and AC at D and E respectively.
Prove that DE||BC.
In the given figure, △ABC is an isosceles triangle in which AB =
AC and a circle passing through B and C intersects AB and AC at D and E respectively.
Prove that DE||BC.
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Solution
ANSWER:
ABC is an isosceles triangle.
Here, AB = AC
∴ ∠ACB = ∠ABC ...(i)
So, exterior ∠ADE = ∠ACB
= ∠ABC [from(i)]
∴ ∠ADE = ∠ABC (Corresponding angles)
Hence, DE || BC
ABC is an isosceles triangle.
Here, AB = AC
∴ ∠ACB = ∠ABC ...(i)
So, exterior ∠ADE = ∠ACB
= ∠ABC [from(i)]
∴ ∠ADE = ∠ABC (Corresponding angles)
Hence, DE || BC
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