Download Practice B 11-4

Name
Date
Class
Practice B
LESSON
11-4 Inscribed Angles
Find each measure.
"
1.
#
—
!
mDEA —
1
'
2.
130°
138°
mQRS 3
—
0
mTSR (
6
4.
—
10°
90.5°
mXVU mVXW 4
—
mGH —
)
2
9°
78°
mFGI &
—
%
$
3.
33°
192°
mCED 5
—
8
.
7
,
5. A circular radar screen in an air traffic control
tower shows these flight paths. Find mLNK.
73°
—
+
.
—
-
Find each value.
*
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6.
&
7.
X—
Y—
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$
#
48°
mCED ,
8.
-
13
y
9.
6
a
A—
'
(
4
1
*
B—
mSRT 77°
2
+
nB —
3
Find the angle measures of each inscribed quadrilateral.
mX 9 X—
10.
8
X—
:
X—
5
4
mZ mW 7
12.
mY mT Z— 6
mU Z —
mV Z —
7
mW Copyright © by Holt, Rinehart and Winston.
All rights reserved.
71°
109°
109°
71°
68°
95°
112°
85°
$
11.
mC #
mD 1
mE %
13.
mF &
A—
.
A—
A—
+
,
90°
90°
90°
90°
mK mL mM mN 28
59°
73°
121°
107°
Holt Geometry
Name
Date
Class
Name
Practice A
LESSON
11-4 Inscribed Angles
2. If inscribed angles of a circle intercept the same arc or are
subtended by the same chord or arc, then the angles are
congruent
half
3. The measure of an inscribed angle is
intercepted arc.
Find each measure.
supplementary
1. If a quadrilateral is inscribed in a circle, then its opposite angles are
.
�
1.
.
�
the measure of its
5.
�
�
�
�
���
30°
140°
���
6.
���
�
15
8.
25
z�
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6.
�
42°
m�VUS �
�
10.
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71°
m�ZWY �
�
�
�
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�
�
13
y�
9.
6
a�
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�
�
m�B �
m�C �
m�D �
m�E �
�
�
120°
90°
60°
90°
�
12.
���
���
���� �
�
�
130°
100°
50°
80°
m�F �
m�G �
m�H �
m�I �
������������
10.
m�X �
� ����������
�
m�W �
m�T �
m�U �
���������� �
����
���
�
12.
�
�
m�V �
�� �
�
��� �
m�W �
�
27
Name
Date
m�Z �
���������
�
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
m�Y �
����������
�
�
105°
Class
Holt Geometry
71°
109°
109°
71°
�
11.
m�D �
m�E �
�
68°
95°
112°
85°
13.
m�F �
�
���������
�
���������
���������
�
�
m�L �
m�M �
m�N �
28
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
Date
Class
Holt Geometry
Inscribed Angle Theorem
_
The measure of an inscribed
angle is half the measure of its
intercepted arc.
�
_
_
Possible answer: It is given that AC � AD. In a circle, congruent
�
�
�
�
�ABC is an
inscribed angle.
�
AC is an
intercepted arc.
� �
chords intercept congruent arcs, so ABC � AED. DC is congruent to itself by
�
the Reflexive Property of Congruence. By the Arc Addition Postulate and the
�
�
�
m�ABC � _1_ m AC
2
�
Addition Property of Congruence, ACD � ADC. �ABC intercepts ADC, so
�
�
�
m�ABC � _1_ mADC. �AED intercepts ACD, so m�AED � _1_ mACD. By
2
2
substitution, m�ABC � m�AED. Therefore �ABC � �AED.
�
�
PQ
RS
_ �_
�
�
Inscribed Angles
If inscribed angles of
a circle intercept the
same arc, then the
angles are congruent.
�
�ABC and �ADC intercept
AC, so �ABC � �ADC.
�
Possible answer: It is given that PQ � RS. By the definition of
�
�
�
�
�
congruent arcs, mPQ � mRS. �PSQ intercepts PQ, and �RQS
�
intercepts RS. So m�PSQ must equal m�RQS. Therefore �PSQ
_ � �RQS.
_
�PSQ
_ and
_�RQS are congruent alternate interior angles of QR and PS.
So QR � PS.
�
An inscribed angle
subtends a semicircle
if and only if the angle
is a right angle.
�
�
�
�
�
�
�
�
Find each measure.
�
�
1. m�LMP and m MN
For each quadrilateral described, tell whether it can be inscribed in a circle. If so,
describe a method for doing so using a compass and straightedge, and draw an example.
2. m�GFJ and m FH
�
�
�
3. a parallelogram that is not a rectangle or a square
110°
cannot be inscribed in a circle
�
4. a kite
�
Can be inscribed in a circle; possible answer: The two congruent
angles of the kite are opposite, so they must be right angles.
Draw a diameter. Draw segments from opposite ends of the
diameter to any point on the circle. Use the compass to copy
one of the segments across the diameter. Draw the fourth side.
36°
�
�
48°
36°
�
�
�
m�GFJ � 55°; m FH � 72°
m�LMP � 18°; m MN � 96°
Find each value.
3. x
5. a trapezoid
Can be inscribed in a circle; possible answer: The pairs of base
angles of a trapezoid inscribed in a circle must be congruent.
Draw any inscribed angle. Use the compass to copy the arc that
this angle intercepts. Mark off the same arc from the vertex of
the inscribed angle. Connect the points.
4. m�FJH
�
�
�
(4� � 9)°
�
(5� � 8)°
�
6. a rhombus that is not a square
�
�
5� °
�
cannot be inscribed in a circle
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
59°
73°
121°
107°
m�K �
�
�
�
Write paragraph proofs for Exercises 1 and 2.
2. Given:
Prove: QR � PS
90°
90°
90°
90°
m�C �
�
�
Reteach
LESSON
11-4 Inscribed Angles
Practice C
LESSON
11-4 Inscribed Angles
1. Given: AC � AD
Prove: �ABC � �AED
�
Find the angle measures of each inscribed quadrilateral.
�
13. Iyla has not learned how to stop on ice skates yet, so she just
skates straight across the circular rink until she hits a wall. She
starts at P, turns 75° at Q, and turns 100° at R. Find how many
degrees Iyla will turn at S to get back to her starting point.
77°
m�SRT �
���������
�
�
Find the angle measures of each inscribed quadrilateral.
�
�
�
�
�
_
�
7.
����������
48°
�
8.
���������
���
����
�
�
����������
�
�
�
73°
�
���
�
m�CED �
11.
�
�
���
��� �������
�
�� �
�
�
�
�
x�
�
9.
10°
90.5°
m�XVU �
Find each value.
�
�
����
�
Find each value.
7.
�
5. A circular radar screen in an air traffic control
tower shows these flight paths. Find m�LNK.
�
�
m�VXW �
�
�
mGH �
���
4.
�
���
�
45°
40°
130°
138°
�
mTSR �
9°
78°
m�FGI �
�
�
�
mQRS �
�
m�IHJ �
�
mGH �
�
2.
���
�
�
���
m�BAC �
�
mFE �
�
mDEA �
�
�
Find each measure.
�
�
�
3.
33°
192°
m�CED �
���
���
4. An inscribed angle subtends a semicircle if and only if the angle is a
right angle
.
���
Class
Practice B
LESSON
11-4 Inscribed Angles
In Exercises 1–4, fill in the blanks to complete each theorem.
�
Date
45°
16.4
29
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
65
30
Holt Geometry
Holt Geometry