MCRBG-0502-PA.qxd
6-26-2001
4:07 PM
Page 30
LESSON
5.2
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 272–278
Use the diagram shown. D is the circumcenter of !ABC.
1. Find the length of DA.
B
2. Find the length of AB.
DC " 2
3. Explain why !ADF ! !BDE.
AC ! BC
D
E
2
C
F
A
Use the diagram shown. V is the incenter of !XWZ.
4. Find the length of VS.
S
5. Find the m"VZX.
6. Explain why !XSV ! !ZTV.
3
20!
T
XW ! WZ
m"WXV " 20!
V
X
Lesson 5.2
VT " 3
W
Y
Z
Complete the constructions described.
7. Draw a large acute scalene triangle !ABC. Construct the perpendicular
bisector of each side. Label the circumcenter D. Measure DA, DB, and
DC.
8. Draw a large obtuse scalene triangle !ABC. Construct the bisector of
each angle. Label the incenter D. Measure the perpendicular distance
from point D to each side of the triangle.
Complete the following sentences with always, sometimes, or
never.
?
9. The perpendicular bisector of a triangle is
the same segment as
the angle bisector.
10. The angle bisectors of a scalene triangle
11. The angle bisectors of a right triangle
?
?
intersect at a single point.
intersect inside the triangle.
12. The perpendicular bisectors of a right triangle
?
intersect inside the
triangle.
Find the indicated measure in each exercise.
13. Find ID.
14. Find BD.
C
C
8
D
10
D
15
I
A
30
B
Geometry
Chapter 5 Resource Book
A
12
12
B
Copyright © McDougal Littell Inc.
All rights reserved.
Answer Key
Practice B
1. 2 2. 4
3. D is circumcenter of !ABC so
AD ! DB, AF ! FC, EC ! EB since all 3 sides
are bisected. Since AC ! BC, you know
1
1
1
1
2 AC ! 2 BC. Also AF ! 2 AC and BE ! 2 BC.
Therefore AF ! BE. By definition of circumcenter, DF # AC and DE # BC. So !ADF and
!BDE are right !’s. So !ADF ! !BDE by HL
Congruence Theorem. 4. 3 5. 20" 6. V is
incenter of !XWZ so VX bisects "WXZ and VZ
bisects "WZX. Since it is given that WX ! WZ you
know "WXZ ! "WZX. It follows that
1
1
2 m"WXZ ! 2 m"WZX, then "SXV ! "TZV and
VX ! VZ because "VXZ ! "VZX. Right "’s
"XSV and "ZTV are !. So !XSV ! !ZTV by
AAS Congruence Theorem.
7.
B
8.
B
D
A
C
Distances from D to
A
C
sides of !ABC are
equal.
DA ! DB ! DC
9. sometimes 10. always 11. always
12. never 13. 6 14. 15
D