circles and the points, segments, lines related to it
DESCRIPTION
A demo lesson focusing the definition of a circle and the geometric figures related to it such as the points, segments, and lines related to it.TRANSCRIPT
THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments
Lines
PICTURE! PICTURE!
Bangui Windmills
by Agnes Manalofrom Google Images
G
O
D
•
•
•
LEO The Lionby stylecraze
from Google Images
V
L
E
S
O
Ziplinefrom Google Images
Y
u
O
DEFINITION
A
Note: A circle is named by its center. The circle above is named circle A or .
A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle.
Using circle A,1. Draw the following points:a. L inside circle A; b. G outside circle A; c. N, I, C, and E on circle A.
LET’S EXPLORE!
POINTS
A
L
Interior points
A
G
AI
E
Exterior points
Points on the circle
C
N
Using circle A,2. Connect the following points:
a. A and I; b. C and N; c. E and C.
LET’S EXPLORE!
SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
RadiusLine segment whose endpoints are the center of a circle and any point on the circle
Definition:
Chord
Line segment whose endpoints are any two points on a circle
Definition:
DiameterLine segment that passesthrough the center of a circle, and whose endpoints lie on the circle
Definition:
3. Compare the measures of the segments AI, AE and AC.4. How is the measure of segment EC related to themeasures of segments AI, AE, and AC?
LET’S EXPLORE!
SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
Note: All radii of the same circle are congruent.The diameter is twice the radius.The diameter is the longest chord in a circle.
Using circle A,3. Draw a line containing the points:
a. E and G; b. I and C;
LET’S EXPLORE!
LINES
G
E
secanttangentC
I
A of
secant a is IC
A of
tangenta is EG
AA
Tangent• A line is tangent to
the circle if it touches it just once. Such a line is called a tangent or a tangent line. The point where the tangent touches the circle is called the point of tangency.
• We can also speak of tangent segments or rays.
Definition:
Secant• A line that intersects
the circle twice is called a secant line or a secant.
• Line segments and rays may also be secants.
• Often, secants are drawn from a point outside of the circle to a point on the circle.
Definition:
Identify each of the following as related to ʘ A.1. A2. RP3. PI4. SR5. IS6. PE7. AR8. SI9. AS10. P
Name each of the following:
1. a circle 2. one interior point3. four exterior points4. four points on the circle 5. center 6. two points of tangency 7. four radii8. a chord9. two diameters10. two tangents11. a secant
Work in pairs and try this!Using the circle at the right, A. Draw: (1) radius HJ; (2) diameter IC; (3) chord IS; (4) a line passing through points H and R; (5) line ST
Work in pairs and try this!Using the circle at the right, B. Connect the points: (6) T and C; (7) C and H (8) H and I
Work in pairs and try this!
Using the circle at the right, C. Name the following: (9) a circle; (10) an exterior point (11) a tangent line (12) a secant line (13) a point of tangency (14 - 16) three radii (17 - 20) four chords (aside from IS or SI)
Answers:
S
CJ
I
H R
T
9. J10. R11. HR or RH12. TS or ST13. H14 -16. HJ or JH IJ or JI CJ or JC17 - 20
HI or IHCT or TCCH or HCST or TS
SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
LINES
G
E
secanttangentC
I
A of
secant a is IC
A of
tangenta is EG
AA
THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments Lines
THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments
THE CIRCLE and the
Geometric Figures Related
to ItPoints