Class 9 Exam > Class 9 Questions > Pick out the incorrect statementa)Sides oppos...
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Pick out the incorrect statement
- a)Sides opposite to equal angles are equal in a triangle
- b)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles
- c)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isosceles
- d)All the altitudes of an isosceles triangle are equal
Correct answer is option 'D'. Can you explain this answer?
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Pick out the incorrect statementa)Sides opposite to equal angles are e...
The altitudes of a triangle are the line segments drawn from each side of the triangle to the angle opposite that side, such that the line segment is perpendicular to the side it is drawn from. In an isosceles triangle, only the altitudes of the legs of equal length in the triangle are congruent.
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Pick out the incorrect statementa)Sides opposite to equal angles are e...
Explanation:
Statement (a): Sides opposite to equal angles are equal in a triangle.
This statement is true and is a property of triangles. According to the angle-side-angle (ASA) congruence criterion, if two angles of a triangle are equal to two angles of another triangle, and the included sides are also equal, then the two triangles are congruent. Therefore, if two angles of a triangle are equal, the sides opposite to those angles must also be equal.
Statement (b): If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles.
This statement is true. In a triangle, if the altitude from a vertex bisects the opposite side, it implies that the two segments created by the altitude are equal. This is because the altitude forms two right triangles, and in a right triangle, the altitude is also the geometric mean between the two segments it divides on the hypotenuse. Therefore, if the altitude bisects the opposite side, the triangle must have two equal sides, making it isosceles.
Statement (c): If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isosceles.
This statement is true. In a triangle, if the bisector of the vertical angle (angle formed by the two equal sides) bisects the base, it implies that the two segments created by the bisector are equal. This is because the bisector divides the angle into two congruent angles, and by the angle-bisector theorem, the segments opposite to those angles are also equal. Therefore, if the bisector of the vertical angle bisects the base, the triangle must have two equal sides, making it isosceles.
Statement (d): All the altitudes of an isosceles triangle are equal.
This statement is incorrect. The altitudes of an isosceles triangle are not necessarily equal. The altitude of a triangle is the perpendicular segment from a vertex to the opposite side. In an isosceles triangle, the altitude from the vertex bisects the base, but it does not necessarily divide the triangle into two congruent right triangles. The lengths of the altitudes can vary depending on the lengths of the sides and the angles of the triangle.
Therefore, the correct answer is option 'D' because all the altitudes of an isosceles triangle are not necessarily equal.
Statement (a): Sides opposite to equal angles are equal in a triangle.
This statement is true and is a property of triangles. According to the angle-side-angle (ASA) congruence criterion, if two angles of a triangle are equal to two angles of another triangle, and the included sides are also equal, then the two triangles are congruent. Therefore, if two angles of a triangle are equal, the sides opposite to those angles must also be equal.
Statement (b): If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles.
This statement is true. In a triangle, if the altitude from a vertex bisects the opposite side, it implies that the two segments created by the altitude are equal. This is because the altitude forms two right triangles, and in a right triangle, the altitude is also the geometric mean between the two segments it divides on the hypotenuse. Therefore, if the altitude bisects the opposite side, the triangle must have two equal sides, making it isosceles.
Statement (c): If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isosceles.
This statement is true. In a triangle, if the bisector of the vertical angle (angle formed by the two equal sides) bisects the base, it implies that the two segments created by the bisector are equal. This is because the bisector divides the angle into two congruent angles, and by the angle-bisector theorem, the segments opposite to those angles are also equal. Therefore, if the bisector of the vertical angle bisects the base, the triangle must have two equal sides, making it isosceles.
Statement (d): All the altitudes of an isosceles triangle are equal.
This statement is incorrect. The altitudes of an isosceles triangle are not necessarily equal. The altitude of a triangle is the perpendicular segment from a vertex to the opposite side. In an isosceles triangle, the altitude from the vertex bisects the base, but it does not necessarily divide the triangle into two congruent right triangles. The lengths of the altitudes can vary depending on the lengths of the sides and the angles of the triangle.
Therefore, the correct answer is option 'D' because all the altitudes of an isosceles triangle are not necessarily equal.
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Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer?
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Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer? 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 Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer?.
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Solutions for Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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ample number of questions to practice Pick out the incorrect statementa)Sides opposite to equal angles are equal in a triangleb)If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isoscelesc)If the bisector of the vertical angle of the triangle bisects the base of the triangle, then the triangle is isoscelesd)All the altitudes of an isosceles triangle are equalCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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