Medians and Altitudes of Triangles
Explore medians and altitudes in triangles, identifying them and understanding their properties.
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Medians and Altitudes of Triangles
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Read each question carefully and answer to the best of your ability. Show your work where necessary.
1. What is a median of a triangle? Describe its key properties.
2. In the triangle below, draw a median from vertex A to the midpoint of side BC. Label the midpoint M.
1. An altitude of a triangle always passes through the midpoint of a side.
True
False
2. The altitude from a vertex is a segment perpendicular to the opposite side.
True
False
1. A median connects a vertex of a triangle to the of the opposite side.
2. An altitude of a triangle is a segment from a vertex to the opposite side.
3. Every triangle has exactly medians.
1. Which of the following is NOT a property of an altitude?
It forms a right angle with the opposite side.
It connects a vertex to the midpoint of the opposite side.
It can be inside, outside, or on the triangle.
There are three altitudes in every triangle.
2. In an equilateral triangle, what can be said about its medians and altitudes?
Medians and altitudes are always different segments.
Medians and altitudes are the same segments.
Only one median is an altitude.
Equilateral triangles have no altitudes.
1. Consider a triangle ABC with vertices A(1,5), B(5,1), and C(1,1).
a) Plot the triangle on the coordinate plane below.
b) Find the midpoint of side BC. Label it M.
c) Draw the median from vertex A to point M.
d) Draw the altitude from vertex A to side BC.