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  • 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. 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. 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. • 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. 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. 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. 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. 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. 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. 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. 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