Plane Symmetry Ajay Naik, Abhishek Shah, Saumya Baheti

Introduction- S

Our group has been given the task to analyze, understand and present the plane of symmetry of 3D objects.

We have to connect the information we obtain to our guiding question.

This task is MYP based, and will be graded on the investigate criterion.

Connection of the Guiding Questions to our Syllabus - AJ

Our Guiding Question is: How Is our Reflection in the mirror our true selves?

Objectively, this guiding question seems to be weak, but when you think about it subjectively, a whole new realm of ideas is unleashed.

The guiding question uses our syllabus very carefully, as a metaphor, to connect it to real life.

What is Plane Symmetry? -AS

A plane of symmetry divides a three dimensional shape into two congruent halves that are mirror images of each other.

This means that if you cut a 3-D object from any side or angle and it turns out to be congruent with the other, its called a plane of symmetry.

Why is the Knowledge of Plane Symmetry Important- AJ

Symmetry seems to be such a small aspect of the study of Geometry, however it is an integral component connecting Mathematics to the real world.

Symmetry can be found in everyday items, however the connections to Mathematics are rarely noted.

Symmetry, in the real world, is expressed in many pieces of art, for example, quilts are highly mathematical in their creation, and depict how symmetry and mathematics are linked to real-life uses.

Symmetry aids students in learning how to classify objects according to the arrangement of their constituent parts.

Why is the Knowledge of Plane Symmetry Important- AJ

Ordering and classification are skills that are used throughout many daily tasks, and the ability to notice patterns or similarities will make these tasks much easier to carry out.

The study of symmetry in schools should look beyond geometric forms to organic shapes, meaning animals, plants, and everyday items.

Children learn concepts about geometric shapes at a very early age. They learn, first, about a shape as a whole, but, with the help of symmetry, children learn how to focus on the characteristics and parts of an object.

The teaching of symmetry holds great importance in the development of mathematical minds of students as it gives students a different perspective of the world around them.

Cube- S

It has six flat sides, each of which is a square of the same size, with three meeting at each vertex.

All edges are equal and any two intersection edges form right angles.

A cube is also a prism, because it is a square throughout its length.

It is also called a regular hexahedron.

Cube - S

Cuboid - AJ

It has six flat sides and all angles are right angles.

And all of its faces are rectangles.

It is also a prism because it has the same cross-section along a length.

Its known commonly as a rectangular prism.

Volume: Breadth x Width x Height.

Surface Area: 2wl + 2lh + 2hw

Cuboid

3 Planes of symmetry

Triangular Prism- AJ

There are 6 lines of symmetry.

The three side faces are triangles and the base shape is a triangle.

4 Vertices

6 Edges

Volume: 1/6 Height x Width x Breadth

Surface Area: l

Triangular Pyramid- S

The tetrahedron has 4 vertices, 6 edges and 4 faces, each of which is an equilateral triangle.

There are 6 planes of reflectional symmetry, one of which is shown on the below. Each such plane contains one edge and bisects the opposite edge.

Triangular Pyramids

Regular Tetrahedron: 6 planes of symmetry

Square Pyramid- AJ

A square based pyramid is a very interesting object.

It has 4 planes of symmetry:

The 4 Side Faces are Triangles

The Base is a Square

It has 5 Vertices (corner points)

It has 8 Edges

Surface Area = [Base Area] + 1/2 × Perimeter × [Slant Length]

Volume = 1/3 × [Base Area] × Height

A square based pyramid has 4 planes of symmetry.

Sphere - AB

A sphere will have infinite planes of symmetry through the center of the sphere since you can cut it through the center and both parts are equal.

Circular cone - S

A cone is a 3 dimensional geometric shape that tapers from a round base to a point called the vertex/apex.

Its base is circular, and circles have infinite lines of symmetry, therefore cones have infinite lines of symmetry when we dissect it vertically through its vertex, perpendicular to the base.

Cylinder - AB

Two of the faces of a cylinder are circles.

Circles have an infinite number of lines of symmetry.

Therefore cylinders have an infinite number of planes of symmetry.

Reflection

This MYP Assessment has helped me learn a lot. This assessment. This assessment made me realize the importance of MYP, and how helpful it is. By completing this assignment, I have gained skills in many areas:

Problem Solving: My friends and I overcame many problems that arose during the process of our presentation.

Team-Work: Whatever work we have done, and whatever problems we have overcome, we have done it as a team.

Critical thinking: We used critical thinking to analyze our guiding question, and work around it.

Reflection

I would connect this assessment to the AOI Human Ingenuity. I believe this Is appropriate, because this topic, and the guiding question itself, is derived from the critical thinking skills that humans have been rewarded with.

I believe that working with my teammates has been a pleasure. I truly want to commend the organizational skills, and the quick, intuitive thinking that both my peers, Saumya, and Abhishek clearly displayed during the course of the assignment. I look forward to getting more opportunities to work with them in the near future.