Basic Geometry and 2D Shapes Study Notes

In 1st grade, we learn all about basic shapes! We will explore what makes a shape, how to name different shapes, and even how to put them together or break them apart. Let's dive into the world of geometry!

🌟 What are 2D Shapes?

2D shapes are flat shapes that you can draw on a piece of paper. They only have length and width, but no thickness. Think of them like a picture!

Key Idea: 2D shapes are flat! They are also called "plane shapes."

📌 Important Parts of a Shape

Every 2D shape has special parts that help us describe it:

• Sides: These are the straight lines that make up the shape.
• Vertices (or Corners): These are the points where two sides meet.

Let's look at an example:

A triangle has:

• 3 sides
• 3 vertices (corners)

We can count them to understand each shape better!

🌈 Common 2D Shapes We Know

Here are some of the most common 2D shapes you will learn about:

🟠 Circle

A circle is a round shape. It has:

• 0 sides (it's curved all around!)
• 0 vertices (no corners)

Think of a clock face or a pizza!

🔺 Triangle

A triangle is a shape with three straight sides. It has:

• 3 sides
• 3 vertices

Like a slice of pizza or the top of a party hat!

🟦 Square

A square is a special shape with four straight sides. All its sides are the same length! It has:

• 4 sides (all equal in length)
• 4 vertices

Think of a cracker or a checkerboard square!

🟩 Rectangle

A rectangle is also a shape with four straight sides and four vertices. Unlike a square, its sides are not all the same length. It usually has two long sides and two short sides. It has:

• 4 sides
• 4 vertices

Like a door or a book!

🟨 Hexagon

A hexagon is a shape with six straight sides. It has:

• 6 sides
• 6 vertices

Think of a stop sign or a honeycomb cell!

📏 Comparing 2D Shapes

We can compare shapes by looking at their attributes:

Shape	Number of Sides	Number of Vertices
Circle	0	0
Triangle	3	3
Square	4	4
Rectangle	4	4
Hexagon	6	6

➕ Making New Shapes (Composing Shapes)

You can put smaller shapes together to make bigger, new shapes! This is called composing shapes.

Example:

• You can put two triangles together to make a square or a rectangle.
• Two squares can make a larger rectangle.
• You can use six triangles to make a hexagon.

It's like building with blocks, but with flat shapes!

➖ Breaking Apart Shapes (Decomposing Shapes)

Just like you can put shapes together, you can also break a larger shape into smaller shapes. This is called decomposing shapes.

Example:

• A rectangle can be broken into two smaller rectangles.
• A hexagon can be broken into six triangles.
• A square can be broken into two triangles by drawing a line from one corner to the opposite corner.

➗ Equal Shares: Halves and Fourths

Sometimes we need to share shapes equally. We can divide circles and rectangles into equal parts.

🍰 Halves (2 equal shares)

When you divide a shape into two equal parts, each part is called a half. If you have a whole pizza and cut it in half, you get two pieces that are exactly the same size. We can write one half as \( \frac{1}{2} \).

Example: A rectangle cut in half will have two pieces of the same size.

🍕 Fourths or Quarters (4 equal shares)

When you divide a shape into four equal parts, each part is called a fourth or a quarter. If you have a whole pizza and cut it into four equal parts, each piece is a fourth. We can write one fourth as \( \frac{1}{4} \).

Example: A circle cut into four equal pieces.

💡 Understanding Equal Shares

It's very important that the shares are equal! This means each part is exactly the same size. If the parts are not the same size, they are not halves or fourths.