Medians and Altitudes of Triangles
Explore the properties of medians and altitudes in triangles with this Grade 8 geometry worksheet.
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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 all your work where applicable.
1. What is a median of a triangle?
A segment from a vertex perpendicular to the opposite side.
A segment connecting the midpoints of two sides.
A segment from a vertex to the midpoint of the opposite side.
A segment that bisects an angle.
2. The intersection point of the medians of a triangle is called the:
Orthocenter
Incenter
Centroid
Circumcenter
3. An altitude of a triangle is a segment from a vertex to the opposite side (or the line containing the opposite side).
4. The point where the three altitudes of a triangle intersect is known as the .
5. Consider a triangle ABC with vertices A(1, 5), B(6, 5), and C(3, 1). Sketch the triangle and draw one median from vertex A to the midpoint of BC. Label the midpoint M.
6. In triangle PQR, if segment QS is an altitude, what can you conclude about the angle at S?
7. Every triangle has exactly three medians.
True
False
8. In an obtuse triangle, the orthocenter lies outside the triangle.
True
False
9. Draw an acute triangle and label its vertices D, E, F. Then, draw all three medians and label their point of concurrency G (the centroid).
10. Draw an obtuse triangle and label its vertices X, Y, Z. Then, draw all three altitudes and label their point of concurrency H (the orthocenter). You may need to extend the sides of the triangle.