Where do the perpendicular bisectors of an obtuse triangle intersect?
Where do the perpendicular bisectors of an obtuse triangle intersect?
All three bisectors still meet at the same point, but in the acute triangle they meet at a point INSIDE the triangle; with the obtuse triangle they meet at a point OUTSIDE of it.
Does a perpendicular bisector go through a vertex?
So the perpendicular bisectors were from the midpoint, were lines that bisect the sides, and they are perpendicular, but don’t necessarily go through the vertices. When we talk about medians, we are talking about points that bisect the sides, but they go to the vertices, and they’re not necessarily perpendicular.
How do you prove a perpendicular bisector?
A line that splits another line segment (or an angle) into two equal parts is called a “bisector.” If the intersection between the two line segment is at a right angle, then the two lines are perpendicular, and the bisector is called a “perpendicular bisector”.
Can you bisect an obtuse angle?
Any angle, including obtuse, can be bisected by constructing congruent triangles with common side lying on an angle’s bisector.
How do you construct an obtuse angle?
Construction
- Draw a horizontal line segment from point to by a ruler.
- Use protractor and mark a point at an obtuse angle.
- Take a compass and set it to any length by a ruler.
- Finally, join the points and by a line for completing the construction of a triangle geometrically.
Why does a perpendicular bisector work?
The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. Each point on the perpendicular bisector is the same distance from each of the endpoints of the original line segment.
What effect does a perpendicular bisector have on the vertex angle of an isosceles triangle?
The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. The Triangle Sum Theorem states that the three interior angles of any triangle add up to 180 degrees.
