A Detailed Lesson Plan in Mathematics
Grade 10-2
Learning Competency: Proves theorems related to chords, arcs and central angles.
I. Objectives: At the end of the lesson, the students are expected to be able to:
a. define central angles, arcs and chords,
b. determine relationship between minor arc and major arc,
c. apply the arc addition postulate in solving problems involving circles, and
d. prove theorems involving arcs and chords.
II. Subject Matter
a. Topic: Central Angles, Arcs, and Chords
b. Reference: SAP Education. 2014. Synergy for Success in Mathematics - New
Edition. Singapore Asia Publishers Pte Ltd.
c. Materials: Chalk and Board
Marker
Manila Papers
Teaches Activity
A. Preliminary
1. Daily Routines
a. Greetings
b. Checking of orderliness and
neatness of the class and the classroom.
c. Implementing of House Rules.
Students' Activity
B. Pre - Lesson Activities
1. Review
a. Have the students recall
about their last topic on introduction of
circles.
b. Emphasize that last time
they focused more on the outside
properties of a circle.
C. Lesson Proper
1. Given a circle ABC, discuss what
are central angles.
Prepared By: SUPANGA, Joe Angelo D.
2. Recall the basic terms of a circle.
3. Then discuss what is a minor arc.
4. Show what are major arcs.
5. Differentiate the property of the
two arcs.
6. Emphasize the proper labeling of
the minor and major arcs.
7. Add a point D on the circle then
have the students determine 2 minor and
major arcs.
8. Add another line that bisects the
circle and discuss semicircles.
9. Emphasize central angles of an
arc and show that minor arcs are less than
180 degrees, major arcs are greater than
180 and semicircles are equal.
10. Using the same figure, discuss
Adjacent non-overlapping arcs.
11. Test the student by asking if the
pair of minor arc and major arc forming the
circle is considered adjacent nonoverlapping arcs.
12. Emphasize the definition why it is
false.
13. Assign values to some of the
1-2: AB, BC, CD, AD
3-4: ABC, BCD, ACD, ABD
5. False
Prepared By: SUPANGA, Joe Angelo D.
central angles then show that the values
for the other can be obtained by angle
addition, and same will be applied with the
arcs.
14. Emphasize that all arcs within the
circle must add up to 360 arc degree.
15. Referring to the same figure,
discuss congruent arcs.
16. Using another figure, show
relationship between arcs and chords.
i. AB is the arc of chord AB and
AB is the chord of arc AB.
17. Point out that congruent chords
have congruent arcs and vice versa.
18. Bisect the chord by a diameter.
19. Emphasize point m is a midpoint
of arc AB using definition.
20. Ask students whether it’s true that
if the minor arc is bisected by a diameter
then the other major arc is also bisected.
21. Explain answer by using theorem
4.5.
True
D. Generalization
Briefly discuss the key points and
definitions of:
Central Angles
Arcs Minor and Major Arcs
Semicircle
Central Angle of Arcs
Adjacent Non-Overlapping Arcs
Arc Addition Postulate
Prepared By: SUPANGA, Joe Angelo D.
Midpoints and Bisectors
E. Assessment
Given a circle, Find the following:
3 Minor Arcs
3 Major Arcs
A Semicircle
Central Angle of Arc
F. Agreement
Read on the next topic
Prepared By: SUPANGA, Joe Angelo D.