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The side BC of a triangle ABC is produced to D. If the bisector of angle A meets BC at point L. Prove that angle ABC+ACD=2angle ALC?
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The side BC of a triangle ABC is produced to D. If the bisector of ang...
Proof:

  • Draw a line perpendicular to AD through L and let it intersect AD at point E.

  • Let angle ALC = x, angle ABC = y, and angle ACD = z.

  • By the angle bisector theorem, BL/LC = AB/AC.

  • Therefore, BL/AB = LC/AC = (BL+LC)/(AB+AC) = BC/AC.

  • Thus, triangle ABL and triangle ALC are similar.

  • Therefore, angle ALC = x and angle BAL = y-x.

  • Since triangle ABD is a straight line, angle ABD = 180-y.

  • Therefore, angle ACD = z = 180-x-(180-y) = y-x.

  • Thus, angle ABC ACD = 2x = 2angle ALC.

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The side BC of a triangle ABC is produced to D. If the bisector of ang...
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The side BC of a triangle ABC is produced to D. If the bisector of angle A meets BC at point L. Prove that angle ABC+ACD=2angle ALC?
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The side BC of a triangle ABC is produced to D. If the bisector of angle A meets BC at point L. Prove that angle ABC+ACD=2angle ALC? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The side BC of a triangle ABC is produced to D. If the bisector of angle A meets BC at point L. Prove that angle ABC+ACD=2angle ALC? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The side BC of a triangle ABC is produced to D. If the bisector of angle A meets BC at point L. Prove that angle ABC+ACD=2angle ALC?.
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