The learner demonstrates demonstrates understanding understanding of key concepts concepts of circles.
Performance Standards: The learner is able to formulate and find solutions to challe challeng nging ing situa situatio tions ns involv involvin ing g circl circles es and and other other relat related ed terms terms in othe otherr diffe differen rentt disci discipl pline ines s thro through ugh appropriate and accurate representations. Learning Competencies: The learner 1. Derive Derives s induc inductiv tively ely the the relati relation ons s among among chord chords s arcs arcs centr central al angles and inscribed angle. !. Prove Proves s theo theore rems ms relat related ed to chords chords arcs arcs centra centrall angle angles s and and inscribed angles. ". #llustrates #llustrates secants secants tangents tangents segments segments and sectors sectors of of a circle. circle. $. Proves Proves theorems theorems on secan secants ts tangen tangents ts and segment segments. s. %. Solve Solve pro proble blems ms on circ circles les.. WORKTEXT MODULE MAP
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Circles and their Properties
C#(CL)S
Demonstrates kno'ledge and skills related to circles arcs angles tangent lines tangent circles and angles formed by tangent and secant lines .
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LESSON IA.
#dentify and describe terms related to circles. Determine the degree measure of an arc of a circle. Define and identify a central angle. Determine the measure of a central angle. Define and identify an inscribed angle. Determine the measure of an inscribed angle. State and apply the properties of a line tangent to a circle. Determine the measure of the angle formed by tangent and&or secant lines. Solve problems on circles.
CHORDS, ARCS AND CENTRAL ANGLES
*b+ectives: 1. (ecall (ecall the diff differen erentt terms relat related ed to circle circles. s. !. Define Define and and identify identify a minor minor arc and and a ma+or ma+or arc. arc. ". Define Define and and ident identify ify a central central angle. angle. $. Determin Determine e the meas measure ure of of a centra centrall angle. angle.
,ctivity 1
,ctivity 1. - Circles )very'herePurpose :
1. #dentify& name ob+ects found inside or outside the classroom 'hich are circular in shapes. !. Determine the radii diameters circumferences and areas of the given ob+ects 'hich are circular in shapes.
aterials: Tape measure&meter stick&ruler
marking pen
anila paper
masking tape
Procedures: 1. /orm a group 'ith at most five members. !. /ind at least % ob+ects inside or outside the classroom 'hich are circular in shapes then measure each of their radius diameter circumference and area. ". 0rite ans'ers on a manila paper using the table belo'. *b+ect
(adius
Diameter
Circumference
,rea
1. !. ". $. %. $. Present output to the class for discussion. uestions: 1. !. ". $. %.
2o' did you kno' that the ob+ect is a circle3 2o' is the radius related to diameter3 diameter to radius3 2o' did you get the circumference of the ob+ect3 2o' about its 0hat are the usages of these ob+ects3 2o' important are these ob+ects to us3
,ctivity !. 4#dentify ePurpose:
area3
Activity 3 Cent!" An#"e$ !n% Ac$ Concepts: 1.#f the measures of the minor arcs in a circle are e5ual then the measures of their central angles are also e5ual. *r the converse of this statement #f t'o central angles in a circle have e5ual measures then their minor arcs have e5ual measures too. !. #n a circle if t'o minor arcs are e5ual then their corresponding chords are congruent. *b+ectives: 1. To determine measures of central angles using the manipulative circular device. !. To construct central angles using the manipulative circular device given their measures.
Procedures: 1. 0ork in groups of "6% members. 7se the manipulative circular device. !. ,ttach the acetate protractor at the center of the circle using push pin. ". 8oin the center and one push pin on the circumference 'ith a string. 8oin the center and the push pin ad+acent to the first as sho'n in the dra'ing. 2o' many degrees are in the angle made by the string3 Since there are "9 e5ual intervals on the circumference and a complete rotation is "9
̊
°
then 1&"9 of "9
°
; 1
°
<. =ive the measures of the central angles sho'n belo':
C. 7sing the manipulative circular device construct central angles having the follo'ing measures: a. "
°
b. 1!
°
c. !"
°
d. "
°
Determine the measure of each intercepted arc. D. ake a general statement about your findings. ,ctivity $ #nscribed ,ngles and ,rcs
e. ""
°
Concepts: 1. The measure of an inscribed angle is one6half the measure of its intercepted arc. !. #nscribed angles that intercept the same >or congruent? arc are congruent. ". ,n angle inscribed in a semicircle is a right angle. $. *pposite angles of a 5uadrilateral inscribed in a circle are supplementary. *b+ectives: Procedures: 1. 0ork in groups of "6% members. 7se the manipulative circular device. !. ,ttach the acetate protractor at the center of the circle using push pin. ". 8oin the center and one push pin on the circumference 'ith a string. 8oin the center and the push pin ad+acent to the first as sho'n in the dra'ing. 2o' many degrees are in the angle made by the string3 Since there are "9 e5ual intervals on the circumference and a complete rotation is "9
