Triangle Special Segments Worksheet

Triangle Special Segments

Read each question carefully and provide accurate answers. Show all your work for full credit.

1. A   of a triangle is a segment from a vertex to the midpoint of the opposite side.

2. An   of a triangle is a segment from a vertex perpendicular to the opposite side.

3. The point where the three medians of a triangle intersect is called the  .

4. The   of a triangle is equidistant from the three vertices of the triangle.

5. Which special segment is always inside an acute triangle but can be outside an obtuse triangle?

6. In an equilateral triangle, which of the following statements is true?

7. In triangle ABC, AD is a median. If BD = 5x - 8 and CD = 2x + 10, find the length of BC.

8. Triangle XYZ has vertices X(1, 4), Y(5, 2), and Z(3, 6). Find the equation of the altitude from X to YZ.

9. The incenter of a triangle is equidistant from the sides of the triangle.

10. The circumcenter of a right triangle is always located at the midpoint of the hypotenuse.

Match each special segment with its point of concurrency.