A DETAILED LESSON PLAN IN MATHEMATICS FOR THIRD YEAR HIGH SCHOOL
I. Objectives
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. Re Refe fere renc nces es a. Textboo Textbook: k: Oronce, Oronce, O.A O.A & Mendoz Mendoza, a, M. O. EMath(Geometry). 2007. pages 238-243 B. Instr Instruct uctio iona nall Media Media Visual Aids C. Value Values s Integr Integrati ation on accuracy critical thinking • •
III. Learning Learning Strategies Teacher Activity Activity A. Review What was our lesson last meeting? Very Good! What is a parallelogram?
Student Activity
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Our previous lesson was all about quadrilaterals. A quadrilateral is any foursided figure which includes the parallelogram, rhombus, rectangle, trapezoid, and square.
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B. Motivational Activity Do you want a game class? Do you know the game trip to Jerusalem? Okay! The mechanics of the 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. •
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Yes we do. Yes we do. Students follow.
C. Presentation 1. Student – Teacher Interaction Do you have an idea what our lesson is for today? Precisely! But first, what is a parallelogram?
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Our lesson for today is all about properties of parallelogram. A parallelogram is a quadrilateral having 2 pairs of parallel lines. Students follow
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Student does so.
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Maam, that is a diagonal.
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Exactly! A parallelogram is a 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 draw a line segment AC. What do you call this segment in terms of parallelogram? In this illustration, we have the first property which states, “Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.” The following is the proof of this property.
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Given: □ABCD AC is a diagonal. Prove: ∆ABC is congruent to ∆CDA Proof: Statements Reasons 1. □ABCD is a parallelogram. 2. AB // DC, Definition of AD // BC parallelogram. 3. angle 1 is PAIA Congruent to theorem Angle 2 4. angle 3 is PAIA congruent to Theorem angle 4 5. AC is Reflexive congruent to property AC 6. ∆ABC is Congruent to Postulate ∆CDA
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Then the 2nd property is that, opposite sides of a parallelogram are congruent. From the illustration of parallelogram ABCD where ∆ABC is congruent to ∆ADC, which sides are congruent? Why?
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Students follow. From the 1st property, I can say AB is congruent to DC and AD is congruent to BC by CPCTC (congruent parts of a congruent triangle are congruent). From the 1st property also, I can say angle B is congruent to angle D by CPCTC. If diagonal BC is used, then angle A is congruent to angle Cm also by CPCTC. Angle A and angle B are supplementary since they are consecutive angles of parallelogram ABCD which are interior angles on the line segment AB transversal.
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Brilliant! Next the 3 rd property is: opposite angles of a parallelogram are congruent. Which angles are congruent? Why? Yeah! You’re correct! After that the 4th property is that any two consecutive angles of a parallelogram are supplementary. As we observed 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? Magnificent! Now, how about if line segment CD is the transversal, what can you conclude about angle C and angle D? Amazing you’re so brilliant students! And finally, we have the last property which states, “The diagonals of a parallelogram bisect each other.” As a proof of this property consider this parallelogram ABCD. A
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4 Q 3 2 D Given: □ABCD is a parallelogram.
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Angle C ands angle D is also supplementary since they’re consecutive angles of parallelogram ABCD which are interior angles on the line segment AB transversal. Students follow.
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Students follow.
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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 Reasons 1. □ABCD is a parallelogram. 2. Line segment AB Definition of // line segment DC parallelogram 3. Angle 1 is PAIC congruent to Theorem angle 2, angle 3 is congruent to angle 4. 4. Line segment AB Opposite is congruent to of a line segment BC parallelogram 5. ∆ABQ is congruent to Postulate ∆CDQ 6. Line segment AQ CPCTC. Is congruent to line segment CQ, line segment BQ is congruent to
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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?
line segment DQ 2. Synthesis 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 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.
Answer: Angle C and angle R, Angle A and angle E.
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Given: □ELOG is a parallelogram. EL = 5x -5 and GO = 4x+1. Find EL.
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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
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Very Good! Let us hear from group 2.
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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, m
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Wow! Group 3?
3. Generalization To summarize, the ff. are the properties of a parallelogram.
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1. Opposite sides are congruent. Line segment AB is congruent to line segment CD, Line segment AD is congruent to line segment CB 2. Opposite angles are congruent Angle A is congruent to angle C, Angle B is congruent to angle D 3. 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 supplementary 4. Diagonals bisect each other. Line segment AP is congruent to line segment CP, line segment BP is congruent to line segment DP
IV. Evaluation A. Answer the ff. by referring to the figure. Given: □SURE is a parallelogram.
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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
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□BATH is a
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1. Given: BH = 7x-10 AT = 4x-1 Find: BH=_________ 2. Given: HS=10x+7 AS=5x+22 Find: HA
