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# Lesson plan (1)

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### Lesson plan (1)

1. 1. A DETAILED LESSON PLAN IN MATHEMATICS FOR THIRD YEAR HIGH SCHOOLI. Learning Competencies 1. Identify the properties of parallelogram; 2. Apply the properties of parallelogram in problem solving; 3. Relate the properties of the parallelogram to the real world.II. Subject Matter: Properties of Parallelogram A. References a. Textbook: Oronce, O.A & Mendoza, M. O. E-Math(Geometry). 2007. pages 238-243 B. Instructional Media Visual Aids C. Values Integration • accuracy • critical thinkingIII. Learning StrategiesTeacher Activity Student ActivityA. Review • What was our lesson last • Our previous lesson was all meeting? about quadrilaterals. • Very Good! What is a • A quadrilateral is any four-sided parallelogram? figure which includes the parallelogram, rhombus, rectangle, trapezoid, and square. • Great!B. Motivational Activity • Do you want a game class? • Yes we do. • Do you know the game trip to • Yes we do. Jerusalem? • Okay! The mechanics of the • Students follow. game is that there are chairs you are going to sit and one of the chair has a cartolina which has the consequence written there and should do by the person who can sit on that certain chair when the music stops.
2. 2. C. Presentation 1. Student – Teacher Interaction • Do you have an idea what our • Our lesson for today is all about lesson is for today? properties of parallelogram. • Precisely! But first, what is a • A parallelogram is a parallelogram? quadrilateral having 2 pairs of parallel lines. • Exactly! A parallelogram is a • Students follow quadrilateral with both pairs of opposite sides parallel. Consider this parallelogram ABCD, ĀB and CD parallel to each other (AB // CD) and if segments AD and BC are also parallel to each other (AD // BC), then the quadrilateral is a parallelogram. • Now, may I call on Mary Chris to • Student does so. draw a line segment AC. • What do you call this segment in • Maam, that is a diagonal. terms of parallelogram? • In this illustration, we have the • Students follow. first property which states, “Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.” The following is the proof of this property. A B DCGiven: □ABCD AC is a diagonal.Prove: ∆ABC is congruent to ∆CDAProof:
3. 3. Statements Reasons1. □ABCD is a 1. Given.parallelogram.2. AB // DC, 2. Definition of AD // BCparallelogram.3. angle 1 is 3. The PAIA Congruent to theorem Angle 24. angle 3 is 4. The PAIA congruent to Theorem angle 45. AC is 5. Reflexive congruent to property AC6. ∆ABC is 6. ASA Congruent to Postulate ∆CDA • Students follow. • nd Then the 2 property is that, opposite sides of a parallelogram are congruent. • From the 1st property, I can say • From the illustration of AB is congruent to DC and AD is parallelogram ABCD where congruent to BC by CPCTC ∆ABC is congruent to ∆ADC, (congruent parts of a congruent which sides are congruent? triangle are congruent). Why? • From the 1st property also, I can • Brilliant! Next the 3rd property is: say angle B is congruent to opposite angles of a angle D by CPCTC. If diagonal parallelogram are congruent. BC is used, then angle A is Which angles are congruent? congruent to angle Cm also by Why? CPCTC. • Angle A and angle B are • Yeah! You’re correct! After that supplementary since they are the 4th property is that any two consecutive angles of consecutive angles of a parallelogram ABCD which are parallelogram are interior angles on the line supplementary. As we observed segment AB transversal. on the parallelogram ABCD, line segment BC // line segment AD and line segment AB is a transversal. What can you conclude about angle A and angle B? • Angle C ands angle D is also
4. 4. • Magnificent! Now, how about if supplementary since they’re line segment CD is the consecutive angles of transversal, what can you parallelogram ABCD which are conclude about angle C and interior angles on the line angle D? segment AB transversal. • Students follow. • Amazing you’re so brilliant students! And finally, we have the last property which states, “The diagonals of a parallelogram bisect each • Students follow. other.” • As a proof of this property consider this parallelogram ABCD. A 1 B 4 Q 3 2 D C Given: □ABCD is a parallelogram. Line segment AC and line segment BD are the diagonals. Prove: Line segment AQ is congruent to line segment CQ. Line segment BQ is congruent to line segment DQ.Proof: Statements Reasons1. □ABCD is a 1. Given. parallelogram.2. Line segment AB 2. Definitionof // line segment DCparallelogram3. Angle 1 is 3. The PAIC congruent to Theorem
5. 5. angle 2, angle 3 is congruent to angle 4.4. Line segment AB 4. Opposite is congruent to sides of a line segment BCparallelogram5. ∆ABQ is 5. ASA congruent to Postulate ∆CDQ6. Line segment AQ 6. CPCTC. Is congruent to line segment CQ, line segment BQ • 1,2,3,1,….. is congruent to line segment DQ • Students dos so.2. Synthesis • Students do so. • As an activity, please count off, 1-3 start on you. • Group 1 stay here , 2 on that area, & 3 on the last row. • In your group choose your • C A facilitator, secretary and rapporteur. Then the facilitator will come here and get your problem. • Finished? Are you done? Group 1 will be the first to report and so on. Okay! Let’s hear from group 1. E R Use the figure at the right to answer the following: a. What triangles of parallelogram CARE is congruent? Answer: ∆CRE and ∆RCA. b. Which sides of parallelogram CARE are congruent? Answer: Angle C and angle R, Angle A and angle E. • Given: □ELOG is a parallelogram. EL = 5x -5 and GO = 4x+1.
6. 6. Find EL.• Very Good! Let us hear from group 2. E L G O Solution: Use definition of parallelogram. EL = GO 5x-5 = 4x+1 X=6 Thus, EL = 5(6)-5 = 25 • In the figure, □LEOG is a parallelogram, LO = 34.8 and m<EOG=72. Find LR and m<LGO. L E• Wow! Group 3? R G O Solution: The diagonals of a parallelogram bisect each other line segment LO and line segment GE is diagonals. Consecutive angles of a parallelogram are supplementary. Angle EOG and angle LGO are consecutive angles,
7. 7. m<LGO=180-72+108.3. Generalization To summarize, the ff. are theproperties of a parallelogram. A B P D C1. Opposite sides are congruent.  Line segment AB is congruent to line segment CD, Line segment AD is congruent to line segment CB2. Opposite angles are congruent  Angle A is congruent to angle C, Angle B is congruent to angle D3. Any two consecutive angles are Supplementary.  Angle A & angle B are supplementary.  Angle B & angle C are supplementary  Angle C & angle D are supplementary  Angle A and angle D are supplementary4. Diagonals bisect each other.  Line segment AP is congruent to line segment CP, line segment BP is
8. 8. congruent to line segment DPIV. Evaluation A. Answer the ff. by referring to the figure. Given: □SURE is a parallelogram. R E D T U S U 1. If Su = 7, then RE = _________ 2. ∆SUE = _________ 3. ∆SUR = _______ 4. UT = _________ 5. ST = _________ 6. If SE = 12, then RU=________ 7. Angle U = ________ 8. Angle S = ________ 9. SU = ______ 10. If m<S=73, then m<R=_____ 11. If m<E=75, then m<R=________ 12. If m<U=95, then m<E=_______ 13. m<S+m<E=________ 14. If m<S=60, then m<_______=60
9. 9. 15. If m<URS-55, m<ESR=________V. Assignment A. Use the properties of a parallelogram to do what is asked. B A □BATH is a parallelogram.H T S1. Given: BH = 7x-10 AT = 4x-1 Find: BH=_________2. Given: HS=10x+7 AS=5x+22 Find: HAPrepared by:Anjelyn BetalasBSE Mathematics III
10. 10. 15. If m<URS-55, m<ESR=________V. Assignment A. Use the properties of a parallelogram to do what is asked. B A □BATH is a parallelogram.H T S1. Given: BH = 7x-10 AT = 4x-1 Find: BH=_________2. Given: HS=10x+7 AS=5x+22 Find: HAPrepared by:Anjelyn BetalasBSE Mathematics III
11. 11. 15. If m<URS-55, m<ESR=________V. Assignment A. Use the properties of a parallelogram to do what is asked. B A □BATH is a parallelogram.H T S1. Given: BH = 7x-10 AT = 4x-1 Find: BH=_________2. Given: HS=10x+7 AS=5x+22 Find: HAPrepared by:Anjelyn BetalasBSE Mathematics III