Download BIG IDEA - OpenCurriculum

Big Idea:
1. The altitude bisects the base of an isosceles triangle (#1)
2.
The distance that a segment is from a point is measured as a perpendicular distance (#1)
3. The perpendicular bisector of a chord passes through the center of the circle (#2)
If a segment is perpendicular to a chord, then it bisects it (#2)
If a segment bisects a chord, then it is perpendicular to it (#2)
4. If a chord is equidistant from the center of the circle as another chord, the chords are congruent. (#3)
If a chord is smaller than another chord, it is further away from the center of the circle.
If it is larger, it is closer to the center of the circle. (#4)
5. The largest chord of a circle is the diameter (#5)
6. The length of an arc is different than the measure of an arc (#6)
7. An arc measuring less than 180 degrees can be named by 2 letters, an arc named by 3 letters is greater
than 180 degrees. (#6)
8. The measure of an intercepted arc is the same as the measure of its central angle (#6)
9. The measure of an inscribed angle is ½ the measure of its intercepted arc (#9)
10. If two central angles have the same measure, then so do their intercepted arcs. (#6)
If two arcs have the same measure, then so do their central angles (#6)
If 2 chords have the same measure, then so do their central angles and intercepted arcs (#7)
( x − h) 2 + ( y − k ) 2 = r 2
11. The equation of a circle is
(#8)
12. Secants intersect a circle at 2 points. (#10)
13. A tangent intersects a circle at 1 point and is perpendicular to the radius intersecting it. (#10)
14. The slope of a tangent is the negative reciprocal of the slope of the radius/diameter tangent to it (#11)
Geometry Unit 10 Big Idea Problems
_____________________________________
BC
1.
How far is
from
A
Name
A
?
50°
B
50°
10
C
BIG IDEA:
Geometry Unit 10 Big Idea Problems
_____________________________________
2.
dA
Name
with radius of 41.
D
AD ⊥ BC ED = 1
,
BC
C
E
Find
A
BIG IDEA:
B
Geometry Unit 10 Big Idea Problems
_____________________________________
3.
dA
Name
BC
with radius of 5. Which chord is bigger,
or
ED
E
?
3
A
B
BIG IDEA:
D
8
C
Geometry Unit 10 Big Idea Problems
_____________________________________
Name
50
B
C
A
78
E
D
4.
dA
BC
with radius of 65. Which chord is closer to the center of the circle,
or
ED
?
BIG IDEA:
Geometry Unit 10 Big Idea Problems
_____________________________________
5.
Name
Draw in the longest chord of this circle. Justify why you think it is longest and what characteristics it has
that makes it the longest?
BIG IDEA:
Geometry Unit 10 Big Idea Problems
_____________________________________
Name
What is the area of the sector BAC?
A
B
C
120°
4 feet
BIG IDEA:
Geometry Unit 10 Big Idea Problems
_____________________________________
6.
If
» = 110°
KE
, the radius of circle I is 6, and
a. What is the length of
Name
RKIR ≅ 110o
,
E
¼
KER
I
?
K
b. What is the measure of
¼
KER
?
R
c. How do
BIG IDEA:
¼ ¼
KR ER
,
and
¼
KE
compare in measure?
Geometry Unit 10 Big Idea Problems
_____________________________________
7.
If
RKIR ≅ 110o
Find
10 2
,radius =
and
KR = 20
Name
E
EK
I
R
K
BIG IDEA:
(x, y)
5
(7,8)
Geometry Unit 10 Big Idea Problems
Name _____________________________________
8.
a. Write an expression for the length of horizontal segment
b. Write an expression for the length of the vertical segment
c. Write an equation for the relationship of the horizontal and vertical segments as compared to the
hypotenuse
d. Write a general relationship for the equation of a circle not centered at (0,0)
BIG IDEA:
A
C
B
D
Geometry Unit 10 Big Idea Problems
_____________________________________
¼
BDC RCDB
9. Find the measure of
,
Name
¼
DC
and
24
12.5
7
16.9°
BIG IDEA:
Geometry Unit 10 Group Challenge Opener
_____________________________________
Name
Circle Alpha has a radius of 10 centimeters. Circle Beta has a radius of 15 centimeters. A chord of length 8 centimeters is
drawn on each circle. Is the chord on circle Alpha or the chord on circle Beta closer to the center of its circle?
Distance of Chords
Task Card Side #1
Task: Your group’s task is to solve the following 2 problems and justify your work to Mr. Jhunjhunwala in written
form.
Your group will earn today’s point by accurately solving the problem and
providing a clear explanation of your solution.
Individual Accountability: Each group member must have the work completed on their own task card.
Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn
the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you
are ready for Mr. Jhunjhunwala to assess your group’s work, call him over.
Problem #1:
( x − 3)
2
+ ( y − 5 ) = 169
2
The equation for circle A is
( x + 2)
2
+ ( y − 1) = 25
2
The equation for circle B is
A chord of length 24 cm is drawn on circle A. A chord of length 6 cm is drawn on circle B.
Is the chord on circle A or the chord on circle B closer to the center of its circle?
Solution and justification:
Distance of Chords
Task Card Side #2
Task: Your group’s task is to solve the following 2 problems and justify your work to Mr. Jhunjhunwala in written
form.
Your group will earn today’s point by accurately solving the problem and
providing a clear explanation of your solution.
Individual Accountability: Each group member must have the work completed on their own task card.
Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn
the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you
are ready for Mr. Jhunjhunwala to assess your group’s work, call him over.
Problem #2:
( x − 125)
2
+ ( y − 130 ) = 4225
2
The equation for circle A is
A chord of length 120 cm is drawn on circle A. A second chord of length 78 cm is also drawn on circle A.
Which chord is closer to the center of the circle? By how much is it closer?
Solution and justification:
Distance of Chords
CHALLENGE CARD
Task: Your group’s task is to solve the following problem and justify your work to Mr. Jhunjhunwala in written
form.
Your group will earn a bonus point for today by accurately solving the
problem and providing a clear explanation of your solution.
Individual Accountability: Each group member must have the work completed on their own task card.
Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn
the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you
are ready for Mr. Jhunjhunwala to assess your group’s work, call him over.
Problem:
Two chords are ten cm from the center of a circle.
7 x 2 − 15
The first chord has a length of
long is the radius of the circle?
Solution and justification:
16x
. The second chord has a length of
. How long is each cord? How
Geometry Unit 10 Week 1 Group Quiz
_____________________________________
Name
I will select one of your group’s papers, and grade it. This will be the group’s grade on the quiz, so be sure to
check everyone’s work. You will also take a very similar quiz so be sure you agree with and understand all the
problems.
1.
This is a circle w/ center at B.
ABD = 30
Find the measure of each arc. (I am NOT asking you to find the length!!!)
»
AD
»
DC
D
= ______
30°
A
= ______
¼
AEC
¼
DCA
B
8
= ______
E
= ______
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
2.
This is a circle w/ center at F.
H
GH = HI = IJ
J
GK = KJ
» = 54°
GH
Find
G
F
¼
IJK
K
C
(OVER)
3.
A chord is 72 cm long.
The chord is 15 cm from the center of the circle.
How long is the radius of the circle?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
y-axis
x-axis
C
D
B
4.
BD
is a diameter of
B = (0, 12)
eC
D = (8, 12)
Complete the equation for this circle:
( x − ____ )
2
+ ( y − ____ ) = _____
2
Geometry Unit 10 Week 1 Quiz #1
Name _____________________________________
y-axis
x-axis
C
D
B
1.
BD
is a diameter of
B = (0, 7)
eC
D = (20, 7)
Write the equation for this circle:
2.
This is a circle w/ center at B.
ABD = 45
D
Find the measure of each arc. (I am NOT asking you to find the length!!!)
¼
ADC
= ______
45°
A
B
8
E
C
»
DC
¼
AD
= ______
= ______
¼
DCA
= ______
(OVER)
3.
A chord is 48 cm long.
The chord is 7 cm from the center of the circle.
How long is the radius of the circle?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
4.
This is a circle w/ center at F.
H
GH = HI = IJ
J
GK = KJ
¼
GH = 58°
Find
G
F
¼
IJK
K
Geometry Unit 10 Big Idea Problems
Definitions:
Name
A secant line intersects a curve(or circle) in exactly 2 points
A tangent line intersects a curve(or circle) at exactly 1 point
_____________________________________
10. Lines
suur
AB
suur
AC
and
If the radius of circle
a.
are tangent to circle
D
is 7, and
D
.
AD = 25
Find AB
D
C
B
b. Find AC
A
»
CB
CHALLENGE: Find the measure of
BIG IDEA:
Geometry Unit 10 Big Idea Problems
_____________________________________
10. Lines
suur
AB
suur
AC
and
are tangent to circle
D
Name
.
If the coordinates of D are (15, 50) and the coordinates of
B are(22, 26)
a. What is the slope of
BD
?
D
C
B
b. What is the slope of
AB
?
A
CHALLENGE: What are possible coordinates of A?
BIG IDEA:
Geometry Unit 10 Cumulative Problems
_____________________________________
1. Segment
ZY
AB
is tangent to Circle Q at the midpoint of
Name
AB
. Segment
ZY
is tangent to Circle D at the midpoint of
. AB = 18 and ZY = 20. If AQ = 15 and ZD = 14, which circle is larger? Justify your answer.
Geometry Unit 10 Cumulative Problems
_____________________________________
Name
40°
2. Two chords form an inscribed angle that intercepts an arc of measure
angle?
. What is the measure of the inscribed
Geometry Unit 10 Cumulative Problems
_____________________________________
3. A diagonal
XY
and chord
XZ
Name
form an inscribed angle.
PX
of
and the circle is point Z. The measure of arc
YP, YX, and XP.
– 3)
2
+
is
(y
Find: The length of
»
PR
Find: The measure of
»
PR
+ 18 )
2
= 64
QP
.
∠
60°
PSR =
. If the radius of the circle is 5, find the length of
Name
4. The equation of a circle Q is
the circle, and the measure of
is a tangent to the circle at point Y. The intersection
YZ 120°
Geometry Unit 10 Cumulative Problems
_____________________________________
(x
YP
.
QR
and
are both radii. S is another point on
Find: The area of Sector QPR
Geometry Unit 10 Cumulative Problems
_____________________________________
5.
Name
Circle L is four times as big as circle Q. The left side of Circle L is tangent to the right side of Circle Q. Write the
equation of Circle L.