Download Geometry Worksheet 5

Geometry Worksheet 5.1A
Bisectors, altitudes, and medians
Name ________________________
Per ___ Date __________________
1. Name all the parts in the triangle.
a. Median
b. Angle Bisector
c. Altitude
d. Perpendicular Bisector
2. Name all the parts in the triangle.
a. Median
b. Angle Bisector
c. Altitude
d. Perpendicular Bisector
3. Name all the parts in the triangle.
a. Median
b. Angle Bisector
c. Altitude
d. Perpendicular Bisector
4. If E is the midpoint of AB , F is the midpoint of BC , and G is the midpoint of AC , Name
each:
a. The altitudes of ΔABC
b. The medians of ΔABC
5. Underline the correct word or phrase to complete each sentence.
a. Three or more lines that intersect at a common point are called
(parallel/perpendicular/concurrent) lines.
b. Any point on the perpendicular bisector of a segment is (parallel to/congruent
to/equidistant from) the endpoints of the segment.
c. A(n) (altitude/angle bisector/median/perpendicular bisector) of a triangle is a
segment drawn from a vertex of a triangle perpendicular to the line containing the
opposite side.
6.
A.
B.
C.
D.
E.
F.
FJ is what type of segment? ______
Perpendicular Bisector
Altitude
Median
Angle Bisector
A and C
All of the above.
A
7. Given: AO is an altitude and angle bisector
Prove: AO is a median
1. AO is an altitude
2.
3.
4. AO is an angle bisector
5.
6.
7. ΔCOA ≅ ΔBOA
8.
9. AO is a median
1.
B
C
O
2. If altitude then
Create right angles with opposite side.
3.
4.
5. If angle bisector then divides angle into two
Congruent angles.
6.
7.
8.
9.
8. In the proof above, what type of triangle is ΔCAB ?
9. What in real life could you relate the word altitude to so that you could remember
the meaning of the word better?
JJJG
10. BD is the perpendicular bisector of
AC . Find AC.
11. Find x and y, if DE is a median
C
5x-6
D
B
3x+8
A
JJJG
12. Find x if MR bisects (NMP , m(1 = 6 x − 9 ,
and m( 2 = 4 x + 13 .
M
JJJG
13. Find x if MR bisects (NMP , m(1 = 5 x + 8 ,
and m( 2 = 8 x − 16 .
N
2
R
N
1
R
M
P
14. Solve for x.
1 2
P
15. Find AC.
C
x+8
(3x+3)° T
x-9
A
B
BT is an al ti tud e