1. Statement 36: The perpendiculars drawn from the vertices of a triangle to the opposite sides are known as the altitudes of the triangle. Conclusion I: The line segments joining the vertices to the midpoint of opposite sides of a triangle are always perpendicular on that side and are called medians of the triangle. - This conclusion is incorrect because medians join vertices to midpoints but are not necessarily perpendicular to the opposite sides. Conclusion II: The point of the intersection of the three perpendiculars is known as the centroid. - This conclusion is incorrect; the intersection of altitudes is called the orthocenter, not the centroid. 2. Statement 37: A chord which passes through the centre of the circle is called the diameter of the circle. Conclusion I: The diameter is the longest chord of the circle. - This conclusion is correct because the diameter passes through the center and is the longest possible chord. Conclusion II: Diameter divides the circle into a major and a minor segment. - This conclusion is incorrect; the diameter divides the circle into two equal semicircles, not major and minor segments. 3. Statement 38: A line segment with both the endpoints lying on the circle is called the chord of the circle. Conclusion I: A chord of a circle divides the circle into two parts. Each part is called a sector of the circle. - This conclusion is incorrect; the two parts are called segments, not sectors. Conclusion II: A tangent can act as a chord but a chord can never act as a tangent. - This conclusion is incorrect; a tangent touches the circle at exactly one point and cannot be a chord, which has two endpoints on the circle. 4. Statement 39: The area bounded by two radii and their corresponding arc is called the sector of a circle. Conclusion I: The diameter of a circle divides the circle into two exactly equal sectors. - This conclusion is correct; the diameter divides the circle into two semicircular sectors. Conclusion II: If the arc of a sector is less than the semicircle, then it is called the major sector. - This conclusion is incorrect; if the arc is less than a semicircle, the sector is called a minor sector. 5. Statement 40: The sum of the angles of a triangle is always 180°. Conclusion I: A triangle in which one of the angles measures 90° is called a right-angled triangle or simply a right triangle. - This conclusion is correct. Conclusion II: A triangle cannot have two or more right angles. - This conclusion is correct because the sum of angles is 180°, so two right angles would exceed this. Final summary: - Correct conclusions: 37.I, 39.I, 40.I, 40.II - Incorrect conclusions: 36.I, 36.II, 37.II, 38.I, 38.II, 39.II