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Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.?
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Prove that the bisector of the vertical angle of an isosceles triangle...
Proof that the Bisector of an Isosceles Triangle Bisects the Base at Right Angles
Given: An isosceles triangle ABC with AB = AC
To Prove: The bisector of the vertical angle at A bisects the base BC at right angles
Proof:
- Construct the bisector of angle A, meeting BC at D
- Since AB = AC (given that it is an isosceles triangle), angles B and C are equal
- Therefore, angles ABD and ACD are equal since the bisector of angle A divides angle BAC into two equal angles
- Triangles ABD and ACD are congruent by the ASA (angle-side-angle) criterion
- Therefore, BD = DC (corresponding parts of congruent triangles are equal)
- By definition, the bisector of any angle divides the opposite side into two equal parts
- Hence, the bisector of angle A bisects the base BC at right angles
Conclusion: The bisector of the vertical angle of an isosceles triangle bisects the base at right angles.
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Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.?
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Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.? 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 Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.?.
Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.? 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 Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.?.
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