Transcript GSP Fill In Notes

Geometry Topics
Unit 8 GSP Explorations & Notes
Name: __________________________
Date: ___________________________
Tab 1 – Central Angles and Arcs
Rule: The measure of an intercepted arc is __________ to the measure of its
central angle.
Tab 1 – Central Angles and Arcs
Sketch the Diagram:
Examples: Use Circle Q.
H
Find:
1) mHB = ________
55°
B
3) mCBF = _______
mBQC
4) mBCD = _______
mBKC
5) mBCH = _______
mCQD
mFQG
6) mDFB = _______
mCND
mFMG
7) mCD = ________
mDQF
mGQB
8) mCDH = _______
mDLF
mGJB
F
32°
2) mBHF = _______
Fill in the measurements:
Q
C
D
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 1 Quia Quiz. Complete the quiz.
Tab 2 – Tangents & Radii
Rule: If a line is tangent to a circle, then the line is _____________________
to the radius drawn to the point of tangency.
Sketch the Diagram:
Example – Use circle Q with point of tangency A.
Tab 2 – Tangents and Radii
Classify DQAB by angles: ______
What is the length of the radius
of Circle Q? ________________
Q
QA = _________
QC = _________
C
Fill in the measurements:
mQAB
A
QA = 10
B
AB = 24
Find QB. ___________________
Find CB. ___________________
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 2 Quia Quiz. Complete the quiz.
Geometry Topics
Unit 8 GSP Explorations & Notes – page 2
Name: __________________________
Date: ___________________________
Tab 3 – Tangent Segments from a Point
Rule: Segments that are tangent to a circle from a point are _________________.
Tab 3 – Tangent Segments from a Point
Example 1 (B and C are points of tangency):
B
Sketch the diagram:
A
Classify DBAC by sides?
_______________________
mBAC = 32
C
mABC = ________
mBCA = ________
Example 2:
Fill in the Measurements:
B
B and C are points of tangency.
x + 10
x = __________
BA
A
BA = _________
BC
C
CA = _________
3x + 2
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 3 Quia Quiz. Complete the quiz.
Tab 4 – Inscribed Angles & Arcs
Tab 4 – Inscribed Angles and Arcs
Inscribed Angle: ______________________________________________________
___________________________________________________________________
___________________________________________________________________
Sketch the Diagram
Rule: The measure of an inscribed angle is equal to ____________
the measure of its intercepted arc.
Example:
mGFJ = ________
G
F
Fill in the Measurements:
mABC
mADC
mABC
mADC
92°
44°
mHJ = __________
mFG = __________
J
109°
H
mFGH = _________
mFHG = _________
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 4 Quia Quiz. Complete the quiz.
Geometry Topics
Unit 8 GSP Explorations & Notes – page 3
Name: __________________________
Date: ___________________________
Tab 5 – Inscribed Angles Corollary 1
Rule: Inscribed Angles that intercept the same arc are ___________________.
Tab 5 – Inscribed Angles Corollary 1
Sketch the diagram:
Example:
C
B
mAE = 102
mABE = __________
mACE = __________
D
Fill in the Measurements:
mADE = __________
A
mABD
mACD
mBD = 129
E
mAED
mBAD = __________
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 5 Quiz. Complete the quiz.
Tab 6 – Inscribed Angles Corollary 2
Tab 6 – Inscribed Angles Corollary 2
Rule: An angle inscribed inside of a semicircle is a _____________ angle.
Sketch the Diagram
(include measurement):
Examples: (AB is a diameter of each circle). (Round all decimal answers
to the nearest tenth.)
C
y°
A
w°
x°
Q
z°
mBD = 80
B
mBC = 80
mADB = _____ mACB = _____
w = _________ x = __________
y = _________
z = __________
D
AB = 26, AD = 24, DB = ________
D
Complete:
AB is a _______________.
ACB is a _______________.
B
A
mDBA = ______ mDAB = _____
HINT: For the angles you have to use trigonometry.
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 6 Quiz. Complete the quiz.
Geometry Topics
Unit 8 GSP Explorations & Notes – page 4
Name: __________________________
Date: ___________________________
Tab 7 – Inscribed Angles Corollary 3
Rule: If a quadrilateral is inscribed in a circle, then its opposite angles are _______________.
Tab 7 – Inscribed Angles Corollary 3
Sketch the Diagram
(include four angle
measurements):
Example:
Find:
mJKL = __________
M
J
mKLM = __________
mMJK = ___________
K
mJK = _____________
L
mLMJ = 73 mMJK = 88
mMLK = ____________
mLMJ = ____________
mMJ = 102
mLMK = ____________
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 7 Quiz. Complete the quiz.
Tab 8 – Angles formed by Two Tangents
RULE: Angle = ½(Bigger Arc – Smaller Arc)
A and B are points of tangency.
A
Tab 8 – Angles formed by Two Tangents
mADB = ½(m______ - m______)
C
E
D
NOTE: mACB + mAEB = _________.
B
Example 1:
B and C are points of tangency.
Example 2:
B
A
D
mBDC = 200
C
mBC = 116
B
mBC = _________
mCAB = _______
mBDC = _______
mCAB = ______
D
A
C
B and C are points of tangency.
Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 8 Quiz. Complete the quiz.
Geometry Topics
Unit 8 GSP Explorations & Notes
Answers to the Example Problems
Name: __________________________
Date: ___________________________
Tab 1 – Central Angles and Arcs
1) mHB = 55
5) mBCH = 305
2) mBHF = 180
6) mDFB = 235
3) mCBF = 212
7) mCD = 93
4) mBCD = 125
8) mCDH = 273
Tab 2 – Tangents & Radii
Classify DQAB by angles: Right
What is the length of the radius of Circle Q? 10
QA = 10
QC = 10
Find QB. 26
Find CB. 16
Tab 3 – Tangent Segments from a Point
Tab 4 – Inscribed Angles and Arcs
Example 1:
mGFJ = 46
Classify DABC by sides. Isosceles
mHJ = 88
mBAC = 32
Example 2:
mFG = 71
mABC = 74
x=4
mFGH = 251
mBCA = 74
BA = 14
mFHG = 289
CA = 14
Tab 5 – Inscribed Angle Corollary 1
Tab 6 – Inscribed Angle Corollary 2
Example 1: mADB = 90
mABE = 51
mACE = 51
mADE = 51
mACB = 90
w = 40
x = 40
y = 50
z = 50
Example 2: AB = 26, AD = 24, DB = 10
mBAD = 64.5
mDBA = 67.4 mDAB = 22.6
Tab 7 – Inscribed Angle Corollary 3
mJKL = 107
mMLK = 176
mKLM = 92
mLMJ = 214
mMJK = 184
mLMK = 296
mJK = 82
Tab 8 – Angles formed by Two Tangents
Example 1:
mBDC = 200
mBC = 160
mCAB = 20
Example 2: mBC = 116
mBDC = 244
mCAB = 64