Class 9 Exam  >  Class 9 Questions  >  if the bisector of an exterior angle C is par... Start Learning for Free
if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle
Most Upvoted Answer
if the bisector of an exterior angle C is parellel to AC then prove th...
hey if line bisect ext. angle C then how is it parellel to AC .can u write the question again...
Community Answer
if the bisector of an exterior angle C is parellel to AC then prove th...
Given Information
- Triangle ABC with exterior angle at vertex C.
- The bisector of the exterior angle C is parallel to line AC.
To Prove
- Triangle ABC is isosceles (AB = BC).
Proof Steps
1. Understanding the Geometry
- Let D be the point where the bisector of the exterior angle at C intersects the extension of line AC.
- Since the bisector of the exterior angle is parallel to AC, we have the following relationships based on Alternate Interior Angles.
2. Using Angle Relationships
- Since CD (the bisector) is parallel to AC, we know that:
- Angle ACD = Angle DCB (alternate interior angles).
- Let angle ACB = x. Then, angle ACD = 180 - x (exterior angle).
3. Applying the Angle Bisector Theorem
- The angle bisector divides the exterior angle into two equal parts, hence:
- Angle DCB = Angle ACB = x.
- Therefore, angle DCB = 180 - x.
4. Establishing Equal Angles
- Since ACD = DCB, we have:
- 180 - x = x.
- Solving this gives us:
- 2x = 180, or x = 90 degrees.
5. Conclusion about Triangle ABC
- From the above, we find that angles ACB and DBC are equal.
- Thus, AB = BC (since angles opposite to equal sides in a triangle are equal).
- Therefore, triangle ABC is isosceles.
Final Statement
- Hence, if the bisector of an exterior angle at C is parallel to AC, triangle ABC is indeed isosceles, proving AB = BC.
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
Explore Courses for Class 9 exam

Top Courses for Class 9

if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle
Question Description
if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle.
Solutions for if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle in English & in Hindi are available as part of our courses for Class 9. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle defined & explained in the simplest way possible. Besides giving the explanation of if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle, a detailed solution for if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle has been provided alongside types of if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle theory, EduRev gives you an ample number of questions to practice if the bisector of an exterior angle C is parellel to AC then prove that ABC is an isoscels triangle tests, examples and also practice Class 9 tests.
Explore Courses for Class 9 exam

Top Courses for Class 9

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev