Download Unit 3 Practice Answers

Name
Class
Date
Practice
5-4
Form G
Medians and Altitudes
A
In kABC, X is the centroid.
1. If CW 5 15, find CX and XW. CX 5 10; XW 5 5
W
2. If BX 5 8, find BY and XY. BY 5 12; XY 5 4
X
B
3. If XZ 5 3, find AX and AZ. AX 5 6; AZ 5 9
Y
C
Z
Is AB a median, an altitude, or neither? Explain.
4.
5. A
Median; AB bisects
the opposite side.
B
B
A
Altitude; AB is
perpendicular to the
opposite side.
6.
B
Altitude; AB is
perpendicular to the
opposite side.
Neither; AB is not
perpendicular to nor does
it bisect the opposite side.
7. A
2 B
A
3
Coordinate Geometry Find the orthocenter of kABC.
8. A(2, 0), B(2, 4), C(6, 0) (2, 0)
9. A(1, 1), B(3, 4), C(6, 1) (3, 3)
10. Name the centroid. U
11. Name the orthocenter. X
Q
T
S
U
A
E X
D
F
V
G
C
R
B
H
Draw a triangle that fits the given description. Then construct the centroid and
the orthocenter.
13. acute isosceles nXYZ Sample: See art.
X
12. equilateral nCDE Sample: See art.
C
Centroid and
Orthocenter
E
Centroid
Orthocenter
D
Z
Prentice Hall Gold Geometry • Teaching Resources
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33
Y
Name
5-4
Class
Date
Practice (continued)
Form G
Medians and Altitudes
In Exercises 14–18, name each segment.
A
14. a median in nABC CJ
J
I
15. an altitude for nABC AH
C
H G
B
16. a median in nAHC IH
17. an altitude for nAHB AH or BH
18. an altitude for nAHG AH or GH
19. A(0, 0), B(0, 22), C(23, 0). Find the orthocenter of nABC. (0, 0)
20. Cut a large isosceles triangle out of paper. Paper-fold to construct the
medians and the altitudes. How are the altitude to the base and
the median to the base related? They are the same.
21. In which kind of triangle is the centroid at the same point as the orthocenter?
equilateral
22. P is the centroid of nMNO. MP 5 14x 1 8y. Write expressions
to represent PR and MR. PR 5 7x 1 4y; MR 5 21x 1 12y
M
N
P
Q
R
O
15x2
23. F is the centroid of nACE. AD 5
1 3y. Write expressions
2
to represent AF and FD. AF 5 10x 1 2y; FD 5 5x2 1 y
A
B
F
24. Use coordinate geometry to prove the following statement.
E
D
C
Given: nABC; A(c, d), B(c, e), C(f, e)
Prove: The circumcenter of nABC is a point on the triangle.
Sample: The circumcenter is the intersection of the perpendicular bisectors of a triangle.
e
c 1 f
The midpoints of AB and BC are (c , d 1
2 ) and ( 2 , e). So, the equations of their
f
d 1 e
c 1 f d 1 e
perpendicular bisectors are x 5 c 1
2 and y 5
2 . Their intersection is ( 2 ,
2 ),
which is the midpoint of AC.
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
34