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The statements are given below
1) In a triangle ABC in Which AB =AC The altitude AD bisects BC
2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral
3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC
which of the following are correct?
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The statements are given below 1) In a triangle ABC in Which AB =AC Th...
Statement 1: In a triangle ABC in which AB = AC, the altitude AD bisects BC
- When AB = AC in a triangle, it is an isosceles triangle.
- In an isosceles triangle, the altitude from the vertex angle will bisect the base.
- Therefore, in triangle ABC, the altitude AD will bisect BC.

Statement 2: If the altitudes AD, BE, and CF of triangle ABC are equal, the triangle ABC is equilateral
- In an equilateral triangle, all three altitudes are equal and concurrent at the centroid.
- If the altitudes AD, BE, and CF of triangle ABC are equal, then the triangle ABC must be equilateral.

Statement 3: If D is the midpoint of hypotenuse AC of right triangle ABC, then BD = AC
- In a right triangle, the midpoint of the hypotenuse is equidistant from all three vertices.
- Therefore, if D is the midpoint of AC in right triangle ABC, BD will be equal to AC.
In conclusion, all three statements are correct. Statement 1 is true based on the properties of isosceles triangles, Statement 2 is true based on the properties of equilateral triangles, and Statement 3 is true based on the properties of right triangles. Each statement follows logically from the given conditions and triangle properties.
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The statements are given below 1) In a triangle ABC in Which AB =AC The altitude AD bisects BC2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC which of the following are correct?
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The statements are given below 1) In a triangle ABC in Which AB =AC The altitude AD bisects BC2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC which of the following are correct? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The statements are given below 1) In a triangle ABC in Which AB =AC The altitude AD bisects BC2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC which of the following are correct? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The statements are given below 1) In a triangle ABC in Which AB =AC The altitude AD bisects BC2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC which of the following are correct?.
Solutions for The statements are given below 1) In a triangle ABC in Which AB =AC The altitude AD bisects BC2) If the altitudes AD,BE AND CF OF triangle ABC are equal the triangle ABC is equilateral3) If D is the midpoint of hypotenuse AC of ringle TRIANGLE ABC then BD=AC which of the following are correct? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
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