Altitude of a Triangle Worksheet
Grade 12 Math worksheet focusing on understanding and calculating the altitude of various triangles.
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Altitude of a Triangle
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Read each question carefully and provide clear, precise answers. Show all your work for calculation-based problems.
1. What is the definition of an altitude of a triangle?
A line segment from a vertex to the midpoint of the opposite side.
A line segment from a vertex perpendicular to the opposite side.
A line segment that bisects an angle of the triangle.
A line segment connecting the midpoints of two sides.
2. In an obtuse triangle, where does the altitude from an acute angle vertex lie?
Inside the triangle.
On one of the sides.
Outside the triangle.
It doesn't exist.
3. The point where the three altitudes of a triangle intersect is called the .
4. In a right-angled triangle, two of the altitudes are the of the triangle.
5. Consider a triangle ABC with vertices A(1, 5), B(4, 1), and C(7, 5). Find the equation of the altitude from vertex B to side AC. Show your steps.
6. Draw an obtuse triangle and label its vertices. Then, draw and label all three altitudes for the triangle. Clearly indicate the orthocenter.
7. The orthocenter of an acute triangle always lies inside the triangle.
True
False
8. The length of an altitude can be greater than the length of the side it is drawn to.
True
False
9. An equilateral triangle has a side length of 10 cm. Calculate the length of its altitude. Provide your answer in simplest radical form.
10. The area of a triangle is 48 cm². If one of its sides measures 12 cm, what is the length of the altitude to that side?