Understanding Altitudes and Orthocenter of a Triangle

This video tutorial introduces the concept of altitudes in triangles and the orthocenter, the point where the altitudes intersect. It explains how the orthocenter's position varies with the type of triangle: inside for acute triangles, on the triangle for right triangles, and outside for obtuse triangles. The video also demonstrates how to construct altitudes and discusses the need to extend sides in obtuse triangles. An animation illustrates these concepts, and the video concludes with a preview of constructing altitudes in the next lesson.

What is an altitude in a triangle?

• A line segment from a vertex to the midpoint of the opposite side

• A line segment that is parallel to one side of the triangle

• A line segment that bisects an angle of the triangle

• A line segment from a vertex that is perpendicular to the opposite side

What is the orthocenter of a triangle?

• The point where the altitudes intersect

• The point where the perpendicular bisectors intersect

• The point where the medians intersect

• The point where the angle bisectors intersect

Where is the orthocenter located in an acute triangle?

• At the midpoint of the hypotenuse

• Inside the triangle

• On the triangle

• Outside the triangle

In a right triangle, where is the orthocenter found?

• Outside the triangle

• On the hypotenuse

• Inside the triangle

• On the triangle

Which side of a right triangle is not an altitude?

• The hypotenuse

• The side adjacent to the right angle

• The side opposite the right angle

• The altitude from the right angle vertex to the hypotenuse

In an obtuse triangle, where is the orthocenter located?

• At the midpoint of the longest side

• Outside the triangle

• On the triangle

• Inside the triangle

What must be done to construct an altitude in an obtuse triangle?

• Find the midpoint of the opposite side

• Draw a line parallel to the opposite side

• Bisect the angle

• Extend the opposite side

In an obtuse triangle, why do we extend the opposite side?

• To make the triangle equilateral

• To find the midpoint

• To create a right angle with the altitude

• To bisect the angle

What happens to the orthocenter in an acute triangle as the triangle remains acute?

• It stays on the triangle

• It moves outside the triangle

• It remains inside the triangle

• It disappears

How does the orthocenter's position change in different types of triangles?

• It is always inside the triangle

• It is always outside the triangle

• It varies: inside for acute, on for right, outside for obtuse

• It is always on the triangle