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.

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.

 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 __________.