Altitude of a Triangle Worksheet
Explore the concept of altitude in triangles, including definitions, properties, and construction methods for various triangle types.
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Altitude of a Triangle
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. An altitude of a triangle is a segment from a vertex to the opposite side or to the line containing the opposite side.
2. The point where the three altitudes of a triangle intersect is called the .
3. In a right triangle, two of the altitudes are the of the triangle.
1. In which type of triangle does the orthocenter lie outside the triangle?
Acute triangle
Right triangle
Obtuse triangle
Equilateral triangle
2. What is the relationship between an altitude and the side it intersects?
It bisects the side.
It is parallel to the side.
It is perpendicular to the side.
It forms a 45-degree angle.
1. Consider triangle ABC with vertices A(1, 5), B(6, 5), and C(3, 1). Find the equation of the altitude from vertex C to side AB.
2. In an equilateral triangle with side length 8 cm, calculate the length of an altitude.
1. An altitude of a triangle always lies inside the triangle.
True
False
2. In an isosceles triangle, the altitude to the base is also the median and the angle bisector.
True
False
1. Draw an obtuse triangle and construct one of its altitudes. Label the orthocenter.
2. Explain why the altitude from the vertex angle of an isosceles triangle bisects the base.