Triangle Special Segments Worksheet
Explore and identify the properties of medians, altitudes, angle bisectors, and perpendicular bisectors in triangles with this Grade 12 math worksheet.
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Triangle Special Segments
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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?
Median
Altitude
Angle Bisector
Perpendicular Bisector
6. In an equilateral triangle, which of the following statements is true?
The medians are also altitudes.
The incenter and circumcenter are the same point.
All special segments coincide.
All of the above.
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.
True
False
10. The circumcenter of a right triangle is always located at the midpoint of the hypotenuse.
True
False
Match each special segment with its point of concurrency.
11. Medians
a. Orthocenter
12. Altitudes
b. Centroid
13. Angle Bisectors
c. Incenter
14. Perpendicular Bisectors
d. Circumcenter