MODULE 4

• Discipline


  Good taste<|>Excellence
• Chonalyn L. Tecson is the writer
• Joel J. Estudillo is the cover illustrator
• This is Mathematics Quarter 3: Module 4 - Solving Problems Involving Parallelograms, Trapezoids, and Kites
• This is from the Department of Education, National Capital Region, Schools Division Office, Marikina City
• What I Need to Know

  Solve problems involving parallelograms, trapezoids, and kites
• What I Know


  Solve problems involving parallelograms, trapezoids, and kites
• Solving problems involving parallelograms, trapezoids, and kites

  1. Choose the letter that corresponds to the correct answer

  2. Refer to the given parallelogram, trapezoid, or kite

  3. Solve for the unknown values
• In a parallelogram, any two opposite sides are congruent
• In a parallelogram, any two consecutive angles are congruent
• In a parallelogram, any two opposite angles are supplementary
• The diagonals of a parallelogram bisect each other
• A diagonal of a parallelogram divides the parallelogram into two congruent triangles
• Why does the supporting frame of the camera man consist of collapsible parallelograms?

  Parallelograms allow the frame to be collapsed and expanded easily
• Solving problems involving parallelograms

  1. Given information about angles and sides of a parallelogram

  2. Use parallelogram properties to solve for unknown values
• Solving problems involving rectangles


  1. Given information about perimeter and dimensions of a rectangle

  2. Use formulas to solve for unknown dimensions and area
• Solving problems involving squares

  1. Given dimensions of a rectangle

  2. Determine the largest square that can be cut from the rectangle and solve for its perimeter and area
• Solving problems involving parallelograms, trapezoids, and kites

  1. Given information about angles, sides, and properties of parallelograms, trapezoids, and kites

  2. Use the given information to solve for unknown values
• A trapezoid is a quadrilateral with exactly one pair of parallel sides
• An isosceles trapezoid is a trapezoid with congruent non-parallel sides
• The median of a trapezoid is equal to half the sum of the lengths of the two bases
• Designing a plan for a dream house


  1. Design the parallelogram (rectangle, square) shape of the house

  2. Decide the length and width

  3. Solve for the area
• The front part of the house only needs to be designed
• The design will be evaluated based on a rubric
• Solving for the value of x

  1. Refer to parallelogram MNOP

  2. m∠P = 4x-9

  3. m∠N = 3x+10

  4. Solve for x
• m∠P


  Angle P
• m∠N

  Angle N
• Perimeter of parallelogram MNOP


  MN = 4x +6 cm<|>MP = 3x+2cm<|>MN is twice MP
• Length of MN

  Parallelogram MNOP
• Trapezoid


  Quadrilateral with exactly one pair of parallel sides
• Isosceles trapezoid


  Trapezoid with congruent non-parallel sides
• Median of a trapezoid


  Equal to half the sum of the lengths of the two bases
• Base angles of an isosceles trapezoid

  Congruent
• Sides of an isosceles trapezoid

  Congruent
• Opposite angles of an isosceles trapezoid

  Supplementary
• Area of a trapezoid

  Half the product of the height and the sum of the bases
• Finding the area of a trapezoidal roof

  1. Given: base 1 = 5m, base 2 = 15m, height = 8m

  2. Area = 1/2 * height * (base 1 + base 2)

  3. Area = 1/2 * 8m * (5m + 15m)

  4. Area = 80 m2
• Finding the bases and angles of an isosceles trapezoid

  1. Given: Quadrilateral LOVE is an isosceles trapezoid with LE || OV, UR is the median

  2. If LE = 3x - 7cm, OV = 2x + 1cm, UR = 12cm, find the lengths of the bases

  3. If m∠O = 2x - 9, m∠L = 2x + 5, find m∠E

  4. If one base is twice the other and UR = 6cm, find the lengths of the legs
• Solving problems involving isosceles trapezoids

  1. Given: Quadrilateral POST is an isosceles trapezoid with OS || PT, ER is the median

  2. If OS = 3x - 2, PT = 2x + 10, ER = 14, find the lengths of the bases

  3. If m∠P = 2x + 5, m∠O = 3x - 10, find m∠T

  4. If one base is twice the other and ER = 6cm, find the lengths of the bases

  5. If ER = 8in and one base is 2in more than the other, find the lengths of the bases
• Median of a trapezoid


  The line segment that connects the midpoints of the parallel sides