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Practice Problems ( Wks19)
NAME ______________________
DATE _______________
B
Medians
D
F
G
C
E
A
B
Midsegments
F
D
C
E
A
C
b2
h3
b1
h1
B
Altitudes
h2
b3
A
Angle Bisectors
Perpendicular Bisectors
Honors Geometry
Medians #1
Livingston High School
Mathematics Department
Mr. Lamb, Mr. Memory
NAME _____________________
Medians, Altitudes,
Angle Bisectors,  Bisectors
The point of intersection of the medians of a triangle is called the centroid.
The point of intersection of the altitudes of a triangle is called the orthocenter.
The point of intersection of the angle bisectors of a triangle is called the incenter.
The point of intersection of the perpendicular bisectors of a triangle is called the circumcenter..
Fill in the following with the correct word: (Use the words above for some of the choices.)
1. The __________________ separates the three segments into sub-segments that
have a 2 to 1 ratio.
2. The __________________ is equidistant to the sides of the triangle.
3. When drawing a circle around the vertices of a triangle, locate its _______________
.
4. Which of the points is the center of balance of the triangle? ______________
Why does it balance at this point? ______________________________________
5. The _________________, _________________, and ____________________ are
always collinear on a line called the Euler line.
6. If a triangle has three congruent medians then the triangle is ___________________.
7. If none of the altitudes are congruent, the triangle must be __________________.
8. The _____________________ of a triangle separates the triangle into two triangles
with equal areas.
9. In a triangle, the product of any side and its ____________________ to that side is
equal to the product of any other side and the ___________________ to that side.
The product is always equal to ________________ the area.
10. In a _____________________ triangle, the altitudes do not meet in a point.
11. In a right triangle, the perpendicular bisectors meet at the ____________________
_________________________ while the altitudes meet at the ________________.
12. Any point on the ___________________ of a triangle is equidistant from the adjacent
sides of the bisected __________________.
13. The ____________________________ of a triangle separates the side to which it is
drawn into two segments whose ratio is equal to the ratio of the remaining two sides.
Honors Geometry
Medians #1
Livingston High School
Mathematics Department
Mr. Lamb, Mr. Memory
14. The ___________________________ of a triangle separate the side to which it is
drawn into two segments whose ratio is equal to the ratio of the areas of the two
triangles that are formed.
15. The perpendicular bisectors of a triangle will have one bisector pass through a vertex
of the triangle only if __________________________________________________.
16. The intersection of the _______________________________ of a triangle is the
center of inscribed circle.
17. The intersection of the _______________________________ of a triangle is the
center of circumscribed circle.
18. The _____________________ drawn from the vertex of the right angle of a right
triangle creates two isosceles triangles with equal areas. Explain why. __________
___________________________________________________________________.
19. In an obtuse triangle the ______________________ and _______________________
meet outside the triangle, while the ____________________ and ________________
meet inside the triangle.
20. Any point on the ________________________ is equidistant from the endpoints of
the segment. Any point on the ________________________ is equidistant from the
sides of the angle.
21. Use your knowledge of the Pythagorean Theorem
and the special segments within a triangle to solve
the following problem.
B
In the diagram at right,
AE and BD are altitudes.
AB = 20, BC = 20 and
DE = 12.
a. What is the length of BE? ______
D
b. What is the area of ABC? _______
c. What is the perimeter of ABC? _______
A
C
E
d. What is the length of AD? ________
e. Radius of inscribed circle for ABC = ______
Honors Geometry
Medians #1
Livingston High School
Mathematics Department
Mr. Lamb, Mr. Memory