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W4, , Learning Area, Quarter, , Mathematics, Third, , I. LESSON TITLE, II. MOST ESSENTIAL LEARNING, COMPETENCIES (MELCs), III. CONTENT/CORE CONTENT, IV. LEARNING PHASES, A. Introduction, , B. Development, , Nine, , Solving Problems Involving Parallelograms, Trapezoids, and Kites, Solves problems involving parallelograms, trapezoids and kites M9GE-IIIe-1, , Suggested, Time Frame, 5 minutes, , 90 minutes, , Grade Level, Date, , Learning Activities, In this lesson, we shall focus on solving problems involving the relationship, of sides and angles in parallelograms, trapezoids, and kites using their, properties and different theorems. We need to remember all the definitions,, properties, and theorems that we have already discussed regarding, parallelograms, trapezoids, and kites in the previous lessons., Steps in Geometric Problem Solving:, 1. Read the problem carefully., 2. Recognize the relationship of the given figure., 3. Pay attention to the labels., 4. Use appropriate definition, property, postulate, or theorem., 5. Answer the question., SOLVING PROBLEMS INVOLVING PARALLELOGRAMS, TRAPEZOIDS, AND KITES, 1., , Given: Quadrilateral WISH is a parallelogram, a. If m∠𝑊 = (x + 15)0 and m∠𝑆 = (2x + 5)0, what is m∠𝑊?, m∠𝑊 = m∠𝑆, In a parallelogram, any two, opposite angles are congruent., (x + 15)0 = (2x + 5)0, Substitution, (x – x + 15 – 5)0 = (2x – x + 5 – 5)0, Addition Property of Equality, x = 100, Subtraction and Addition Property, m∠𝑊 = ((10) + 15)0, Substitution, m∠𝑊 = 250, Addition Property, b., , ̅̅̅̅ = 3y + 3 and ̅̅̅̅, If 𝑊𝐼, 𝐻𝑆 = y + 13, how long is ̅̅̅̅, 𝐻𝑆?, ̅̅̅̅, ̅̅̅̅, 𝑊𝐼 ≅ 𝐻𝑆, In a parallelogram, any two, opposite sides are congruent., 3y + 3 = y + 13, Substitution, 3y – y + 3 – 3 = y – y + 13 – 3, Addition Property of Equality, 2y = 10, Subtraction and Addition Property, y=5, Dividing both sides by 2, ̅̅̅̅, 𝐻𝑆 = (5) + 13, Substitution, ̅̅̅̅, 𝐻𝑆 = 18, Addition Property, c., , Quadrilateral WISH is a rectangle, and its perimeter is 56 cm., One side is 5 cm less than twice the other side. What are the, dimensions and how large is its area?, Perimeter of Rectangle = 2L + 2W, Formula for Perimeter of Rectangle, 56 = 2L + 2(2L – 5) cm, Substitution, 56 = 2L + 4L – 10 cm, Distributive Property, 56 + 10 = 6L – 10 + 10 cm, Addition Property of Equality, 6L = 66 cm, Addition Property, L = 11 cm, Dividing both sides by 6, 56 = 2(11) + 2W cm, Substitution, 56 = 22 + 2W cm, Multiplication Property, 56 – 22 = 22 – 22 + 2W cm, Addition Property of Equality, 2W = 34 cm, Subtraction Property, W = 17 cm, Dividing both sides by 2, Area of Rectangle = LW, Formula for Area of Rectangle, Area of Rectangle = 11 cm * 17 cm Substitution, Area of Rectangle = 187 cm2, Multiplication Property

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IV. LEARNING PHASES, , Suggested, Time Frame, , Learning Activities, d., , What is the perimeter and the area of the largest square that, can be formed from Rectangle WISH from the previous, question?, L = 11 cm, Determine the smaller number from, the length and width of the, rectangle, Area of Square = s2, Formula for Area of Square, Area of Square = (11 cm)2, Substitution, Area of Square = 121 cm2, Multiplication Property, 2., , ̅̅̅̅ and ̅̅̅̅, Given: Isosceles trapezoid POST with ̅̅̅̅, 𝑶𝑺//𝑷𝑻, 𝑬𝑹 is its median., ̅̅̅̅ = 3x – 2, 𝑃𝑇, ̅̅̅̅ = 2x + 10 and 𝐸𝑅, ̅̅̅̅ = 14, how long is each base?, a. If 𝑂𝑆, 1, Formula for length of median, ̅̅̅̅ = (𝑂𝑆, ̅̅̅̅ + 𝑃𝑇, ̅̅̅̅ ), 𝐸𝑅, 2, 1, Substitution, 14 = ((3x – 2) + (2x + 10)), 2, 28 = 5x + 8, Combining like terms and, simplifying, 28 − 8 = 5x + 8 − 8, Addition Property of Equality, 5x = 20, Subtraction Property, 𝑥=4, Dividing both sides by 5, ̅̅̅̅, 𝑂𝑆 = 3(4) – 2, Substitution, ̅̅̅̅, 𝑂𝑆 = 10, Multiplication and Subtraction, Property, ̅̅̅̅ = 2(4) + 10, 𝑃𝑇, Substitution, ̅̅̅̅ = 18, 𝑃𝑇, Multiplication and Addition, Property, b. If m∠𝑃 = (2x + 5)0 and m∠𝑂 = (3x – 10)0, what is m∠𝑇?, m∠𝑃 and m∠𝑂 are supplementary, Same Side Interior Angles are, Supplementary, (2x + 5)0 + (3x – 10)0 = 1800, Substitution, (5x – 5)0 = 1800, Addition and Subtraction Property, (5x – 5 + 5)0 = (180 + 5)0, Addition Property of Equality, 5x = 1850, Addition Property, x = 370, Divide both sides by 5, m∠𝑃 and m∠𝑇 are congruent, In a isosceles trapezoid, base, angles are congruent, m∠𝑇 = (2(37) + 5)0, Substitution, m∠𝑇 = 790, Simplify, c., , One base is twice the other and ̅̅̅̅, 𝐸𝑅 is 6 cm long. If its perimeter, is 27 cm, how long is each leg?, 1, Formula for length of median, ̅̅̅̅, ̅̅̅̅ + ̅̅̅̅, 𝐸𝑅 = (𝑂𝑆, 𝑃𝑇), 2, 1, Substitution, 6 = ((x) + (2x)), 2, 12 = 3x, Combining like terms and, simplifying, 𝑥=4, Dividing both sides by 3, Perimeter of Isosceles Trapezoid =, Formula of Perimeter of Isosceles, 2L + B1 + B2, Trapezoid, 27 = 2L + 4 + 2(4), Substitution, 27 = 2L + 12, Multiplication and Addition, Property, 27 – 12 = 2L + 12 – 12, Addition Property of Equality, 2L = 15, Multiplication and Addition, Property, L = 7.5 cm, Dividing both sides by 2

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Suggested, Time Frame, 30 minutes, , IV. LEARNING PHASES, C. Engagement, , Learning Activities, Directions: Illustrate and solve the following problems:, 1., 2., 3., 4., 5., , D. Assimilation, , 30 minutes, , Two consecutive sides of a parallelogram measure 4 m and 9 m,, respectively. What is the perimeter of the parallelogram?, One diagonal of a square measure (2x + 4) in. If the other diagonal, measures 16 in, what is x?, ̅̅̅̅//𝑇𝑆, ̅̅̅̅ and̅̅̅̅̅, ̅̅̅̅ = 12, Given trapezoid QRST with 𝑄𝑅, 𝑈𝑉 as the median. If m𝑄𝑅, ̅̅̅̅ = 24 cm, what is m𝑈𝑉, ̅̅̅̅ ?, cm and m𝑈𝑉, An isosceles trapezoid with a diagonal that measures 42 cm and one leg, measures 23 cm. What is the length of the other diagonal?, ̅̅̅̅ = 10 cm and m𝑂𝐸, ̅̅̅̅ = 18 cm. What is, Given kite HOPE with diagonals m𝐻𝑃, the area of the kite?, , Directions: Solve the following problems. Show your complete solutions., 1. A table cloth is cut into a parallelogram in which two opposite angles, measure (8x – 33)ᵒ and (5x + 15)ᵒ? Find the measures of all the angles., 2. One lateral face of the roof of the school building is trapezoid in shape., One of the bases of this trapezoid is 6 m longer than the other base. Find, the length of the two bases if the median measures 19 m., 3. A rectangular garden has a perimeter of 56 ft. Its length is 5 ft less than, twice the width. What is the area of the garden?, 4. A tabletop is an isosceles trapezoid in shape. The median is 5.5 dm, and, one of its legs measures 2.5 dm. If one of the tabletop bases is, 1 dm more than the other, find its perimeter., 5. The area of the paper used by William in the making of his kite is 60, square inches, and one of its diagonals is 2 inches less than the other, diagonal. Find the lengths of the two diagonals., , V. ASSESSMENT, , (Learning Activity Sheets, Enrichment, Remediation, Assessment to be given, Weeks 3 and 6), , VI. REFLECTION, , for, or, on, , 30 minutes, , Directions: Illustrate the following and solve for what is required. Show your, complete solution., 1., , One side of a rectangle is 3 m more than the other. If the perimeter of, the rectangle is 30 m, what are its dimensions?, a. L = 4 m and W = 7 m, c. L = 6 m and W = 9 m, b. L = 5 m and W = 8 m, d L = 7 m and W = 10 m, 2. A rhombus with a perimeter of 60 in has a side with a length of (8x) in., Find x., a. 1.675, b. 1.875, c. 2.275, d. 7.5, 3. One base of a trapezoid is 4 cm less than twice the other. If the median, measures 13 cm, what is the length of the longer base?, a. 10, b. 12, c. 16, d. 20, ̅̅̅̅//𝑃𝑇, ̅̅̅̅ . If m∠O = (10x + 20)O and m∠P= 8x, 4. Isosceles trapezoid POST with 𝑂𝑆, – 2)O , what is x?, a. 9, b. 10, c. 11, d. 12, ̅̅̅̅ = 8 in and m𝑉𝐸, ̅̅̅̅ =20 in. What is the perimeter, 5. Given kite LOVE which m𝐿𝑂, of the kite?, a. 28 in, b. 34 in, c. 56 in, d. 80 in, 20 minutes, , , , , Prepared by:, , Wilson Ray G. Anzures, , The learners communicate the explanation of their personal assessment, as indicated in the Learner’s Assessment Card., The learner will write their personal insights about the lesson in their, notebook using the prompts below:, I understand that ___________________., I realize that ________________________., I need to learn more about __________., Checked by: Ma. Filipina M. Drio