NAME ________________________ Medians, Angle Bisectors ...
NAME ________________________ Medians, Angle Bisectors
Altitudes Worksheet #6
1. Find the following lengths:
a. BE = ____________
b. DE =______ EF= _______ DF= _______
c. AD = _______ CF = ________
d. BT = _______ CT = ________
e. In (ABC , let AH be the altitude from the vertex A to side BC. Find …
AH = ________ BH = ________
f. How long is EH ? __________
g. How far is T from AB ? __________
h. Which of the following describes BE ? (circle the correct answer(s))
Altitude, median, angle bisector, perpendicular bisector
2. Refer to problem #1 to find the following areas:
a. ( ABC = ________ ( DEF = ________
b. ( BED = ________ ( ATB = ________
c. ( DFT = ________ ( CDT = _______
d. Area of quadrilateral DEFT = __________
e. Area of pentagon AFTDC = __________
3. Find the following based on the triangle at right, with the angle bisectors as indicated.
a. Find BE = ____________
b. BD =______ DC= _______
c. Find PE = _______ BP = ________
d. If circle P intersects AB at point W, find BW = ______ and AW = _____
e. How far is point P from AB ?
f. What is the radius of the circle inscribed in (ABC ?
4. The legs of a right triangle are 15 and 36.
a. How long is the median to the hypotenuse?
b. How long is the shortest altitude? ________ Longest altitude? _________
c. What is the radius of the circumscribed circle? ______ Inscribed circle? _________
d. How far apart are the centers of those circles? __________
Fill in the blanks below to complete the theorems:
5. The medians of a triangle meet at a point which separates each into __________________.
6. The _______________ of an obtuse triangle will never meet.
7. An angle bisector separates the opposite side of the triangle into two segments ___________
________________________________________________________________________.
8. The radius of an inscribed circle can be found by using the formula ___________________.
9. Any point on the ____________________________ is equidistant to its sides.
10. Any point on the ___________________________ is equidistant to the endpoints.
11. The ________________ meet at a point which is the center of balance of the triangle.
12. The vertex of the right angle of a triangle is where the _______________ meet.
13. The ______________________ meet outside a triangle that is _______________.
14. The median of a right triangle is __________________________________.
15. The _________________________ meet at the center of the inscribed circle.
16. The ________________________ meet at the center of the circumscribed circle.
17. The most important theorem about altitudes is that _____________________________.
18. Explain what can be determined by the “Ice Cream Cone “ theorem.
______________________________________________________________________________________________________________________________________________________
19. An equilateral triangle is very special since all three medians are equal, and each is also the __________________, _____________________, and part of the ____________________.
20. When will the angle bisector of an angle intersect the opposite side in the same place that the inscribed circle intersects that side? __________________________________________
-----------------------
B
F
D
T
C
E
A
Given: AB = BC = 30
AC = 48
D, E, and F are midpoints
Given: AB = BC = 30
AC = 48
AD, BE, and CF are angle bisectors of the triangle.
B
[pic]
W
F
D
P
C
E
A
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