where can the perpendicular dissector of an acute triangle intersect? l. inside the triangle ll. on the triangle lll. outside the triangle
A. l only
B. lll only
C. l or lll only
D. l, ll, or lll
The perpendicular bisector of any side of a triangle can intersect the triangle at three possible locations: inside the triangle, on the triangle (at the midpoint of the side), or outside the triangle.
Therefore, the perpendicular bisector of an acute triangle can intersect at all three possible locations: inside the triangle, on the triangle, or outside the triangle.
The correct answer choice is D. l, ll, or lll.
The perpendicular dissector of an acute triangle can intersect in different locations based on the configuration of the triangle.
If the triangle is obtuse or right-angled, the perpendicular dissector will intersect on the triangle.
However, if the triangle is acute, the perpendicular dissector can intersect in any of the following locations:
l. Inside the triangle
ll. On the triangle
lll. Outside the triangle
Therefore, the correct answer is:
D. l, ll, or lll
The perpendicular dissector of an acute triangle can intersect in different locations depending on the properties of the triangle.
To find the answer, we need to understand what a perpendicular dissector is. A perpendicular dissector is a line or segment that passes through the midpoint of one side of a triangle and is perpendicular to that side. In an acute triangle, all angles of the triangle are less than 90 degrees.
Now, let's consider the possibilities:
l. Inside the triangle: If we draw the perpendicular dissector from the midpoint of one side of the acute triangle, it will intersect inside the triangle if the angle opposite to that side is acute (less than 90 degrees). This is because the perpendicular dissector will be shorter than the side opposite to it.
ll. On the triangle: The perpendicular dissector can also intersect on the triangle if the angle opposite to the side from which the dissector is drawn is a right angle (90 degrees). In this case, the perpendicular dissector would coincide with the altitude of the triangle.
lll. Outside the triangle: The perpendicular dissector can intersect outside the triangle if the angle opposite to the side from which the dissector is drawn is obtuse (greater than 90 degrees). In this scenario, the perpendicular dissector will be longer than the side opposite to it.
Combining these possibilities, the answer is:
D. l, ll, or lll, since the perpendicular dissector can intersect inside the triangle, on the triangle, or outside the triangle depending on the properties of the acute triangle.