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Quadrilaterals with parallels? (Parallelograms and Its Variants)

Author:Alexis Sparks

Introduction

Welcome, student-learner! Quadrilaterals are four-sided polygons with four angles (Math.com, 2005a). In this activity, you will deal with the learning competencies of identifying and describing the different kinds of quadrilaterals: square, rectangle, parallelogram, and rhombus; determining the conditions that make a quadrilateral a parallelogram; and proving theorems on the different kinds of parallelogram (rectangle, rhombus, square)(Department of Education, 2016). Such competencies are appropriate for 4th and 9th graders (Department of Education, 2016). You will be playing with quadrilaterals and changing their measurements. Be sure to follow the instructions in every section and answer the questions that follow honestly. The applets in this activity are inspired by the works of Kim, Rosalie83, & McCarthy (n.d.).

Quadrilateral 1

In Plane 1, you will see quadrilateral ABCD, sliders line1 and line2, and checkboxes for sides, angles, diagonals, and diagonal segments. Manipulate the vertices of the quadrilateral and the sliders to transform the quadrilateral. Toggle the checkboxes to show and hide various measurements and figures. You can also scroll your mouse to zoom in and out and move the objects, labels, and field around to avoid overlaps. After such, answer the questions that follow.

Plane 1

Assessment of Quadrilateral Theorems

1. What is/are the relationship/s between sides AB and CD?

Check my answer

2. What is/are the relationship/s between sides AD and BC?

Check my answer

3. What is/are the relationship/s between angles ABC and ADC?

Check my answer

4. What is/are the relationship/s between angles ABC and BAD?

Check my answer

5. What is/are the relationship/s between angles ABC and BCD?

Check my answer

6. What is/are the relationship/s between angles BAD and BCD?

Check my answer

7. What is/are the relationship/s between angles ADC and BAD?

Check my answer

8. What is/are the relationship/s between angles ADC and BCD?

Check my answer

9. What is the relationship between the diagonals of the quadrilateral?

Check my answer

10. Manipulate the quadrilateral and the checkboxes. Have your answers for 1-9 changed after transforming the quadrilateral?

Select all that apply
  • A
  • B
Check my answer (3)

Parallelogram

The quadrilateral in Plane 1 is an example of a parallelogram. Parallelograms are quadrilaterals wherein any two opposite sides are parallel and congruent, any two opposite angles are congruent, any consecutive angles are supplementary, and the diagonals bisect each other (Moise & Downs, 1975). Quadrilaterals 2-4 are special types of parallelograms, which means they also follow the same theorems as parallelograms but with added specifications.

Quadrilateral 2

In Plane 2, you will see parallelogram ABCD, sliders line1 and line2, and checkboxes for sides, angles, and diagonals. Manipulate the vertices of the parallelogram and the sliders to transform the parallelogram. Toggle the checkboxes to show and hide various measurements and figures. You can also scroll your mouse to zoom in and out and move the objects, labels, and field around to avoid overlaps. After such, answer the questions that follow.

Plane 2

Assessment of Parallelogram Theorems

1. What is the measure of the angles?

Check my answer

2. What is/are the relationship/s between sides AB and BC?

Check my answer

3. What is/are the relationship/s between sides BC and CD?

Check my answer

4. What is/are the relationship/s between sides CD and DA?

Check my answer

5. What is/are the relationship/s between sides AB and DA?

Check my answer

6. What is/are the relationship/s between the diagonals?

Check my answer

7. Manipulate the parallelogram and the checkboxes. Have your answers for 1-6 changed after transforming the parallelogram?

Select all that apply
  • A
  • B
Check my answer (3)

Rectangle

The parallelogram in Plane 2 is an example of a rectangle. Rectangles are parallelograms wherein all four angles are right angles (Moise & Downs, 1975), any pair of adjacent sides is perpendicular, and the diagonals are congruent/equal.

Quadrilateral 3

In Plane 3, you will see parallelogram ABCD, slider line1, and checkboxes for sides, angles, and diagonals. Manipulate the vertices of the parallelogram and the sliders to transform the parallelogram. Toggle the checkboxes to show and hide various measurements and figures. You can also scroll your mouse to zoom in and out and move the objects, labels, and field around to avoid overlaps. After such, answer the questions that follow.

Plane 3

Assessment of Parallelogram Theorems

1. What is/are the relationship/s of one side of the parallelogram to all the other sides?

Check my answer

2. What is/are the relationship/s between the diagonals?

Check my answer

3. Manipulate the parallelogram and the checkboxes. Have your answers for 1 & 2 changed after transforming the parallelogram?

Select all that apply
  • A
  • B
Check my answer (3)

Rhombus

The parallelogram in Plane 3 is an example of a rhombus. Rhombi/rhombuses are parallelograms wherein the diagonals are perpendicular (Moise & Downs, 1975) and all four sides are congruent/equal.

Quadrilateral 4

In Plane 4, you will see parallelogram ABCD, slider line1, and checkboxes for sides, angles, and diagonals. Manipulate the vertices of the parallelogram and the sliders to transform the parallelogram. Toggle the checkboxes to show and hide various measurements and figures. You can also scroll your mouse to zoom in and out and move the objects, labels, and field around to avoid overlaps. After such, answer the questions that follow.

Plane 4

Assessment of Parallelogram Theorems

1. What is/are the relationship/s between any side and a side adjacent to it?

Check my answer

2. What is/are the relationship/s of one side of the parallelogram to all the other sides?

Check my answer

3. What is the measure of the angles?

Check my answer

4. What is/are the relationship/s between the diagonals?

Check my answer

5. Manipulate the parallelogram and the checkboxes. Have your answers for 1-4 changed after transforming the parallelogram?

Select all that apply
  • A
  • B
Check my answer (3)

Square

The parallelogram in Plane 4 is an example of a square. Squares are parallelograms wherein all four sides are congruent/equal, any pair of adjacent sides is perpendicular, all four angles measure 90 degrees, and the diagonals are perpendicular and congruent/equal. This makes squares the combination of rhombi and rectangles (Math.com, 2005b).

References

Department of Education. (2016). K-12 Math Curriculum Guide. Retrieved October 1, 2020 from https://www.deped.gov.ph/wp-content/uploads/2019/01/Math-CG_with-tagged-math-equipment.pdf Kim, R., Rosalie83, & McCarthy, H. (n.d.). Exploring the Properties of Quadrilaterals. Retrieved October 2, 2020, from https://www.geogebra.org/m/wA6UwU9k Math.com. (2005a) Quadrilaterals - First Glance. Retrieved October 1, 2020, from http://www.math.com/school/subject3/lessons/S3U2L3GL.html Math.com. (2005a) Quadrilaterals - In Depth. Retrieved October 2, 2020, from http://www.math.com/school/subject3/lessons/S3U2L3GL.html Moise, E., & Downs, F., Jr. (1975). Geometry: Metric Edition. (M. Villarmil, R. Favila, & R. Pieters, Eds.) Quezon City: Addison Wesley Publishing Company, Inc.

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