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 states that the line segments joining the vertices to the midpoint of opposite sides are always perpendicular and called medians. This is incorrect because medians join vertices to midpoints but are not necessarily perpendicular. - Conclusion II states that the point of intersection of the three perpendiculars (altitudes) is known as the centroid. This is incorrect; the intersection of altitudes is the orthocenter, while the centroid is the intersection of medians. 2. **Statement 37:** A chord passing through the center of the circle is called the diameter. - Conclusion I: The diameter is the longest chord of the circle. This is true because the diameter passes through the center and is the maximum length chord. - Conclusion II: Diameter divides the circle into a major and a minor segment. This is true; the diameter divides the circle into two semicircles (major and minor segments). 3. **Statement 38:** A line segment with both endpoints on the circle is called a chord. - Conclusion I: A chord divides the circle into two parts, each called a sector. This is false; 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 is false; a tangent touches the circle at exactly one point and cannot be a chord. 4. **Statement 39:** The area bounded by two radii and their corresponding arc is called the sector of a circle. - Conclusion I: The diameter divides the circle into two exactly equal sectors. This is true; each semicircle is a sector. - Conclusion II: If the arc of a sector is less than the semicircle, then it is called the major sector. This is false; such a sector is called a minor sector. 5. **Statement 40:** The sum of the angles of a triangle is always 180°. - Conclusion I: A triangle with one 90° angle is called a right-angled triangle. This is true. - Conclusion II: A triangle cannot have two or more right angles. This is true because the sum of angles is 180°. **Final answers:** - Statement 36: Conclusion I - False, Conclusion II - False - Statement 37: Conclusion I - True, Conclusion II - True - Statement 38: Conclusion I - False, Conclusion II - False - Statement 39: Conclusion I - True, Conclusion II - False - Statement 40: Conclusion I - True, Conclusion II - True