Geometry - Unit 3 Day 1

Unit 3: Symmetry & Transformations

Day 1: Lines & Point Symmetry

Essential Question: How can symmetry be used to describe geometric figures?

Today's Goals

🎯 I will be able to locate, count, and draw lines of symmetry.

🎯 I will be able to determine if a figure has point symmetry, line symmetry, both, or neither.

Key Vocabulary

  • Symmetry: When a figure can be mapped onto itself by a transformation (like a reflection or rotation).
  • Line Symmetry (or Reflectional Symmetry): Exists when a figure can be divided by a line into two parts that are mirror images of each other. The line is called the line of symmetry.
  • Point Symmetry (or Rotational Symmetry of 180°): Exists when a figure looks exactly the same after being rotated 180° around a center point.

I Do: Understanding Line Symmetry

A figure has line symmetry if you can fold it along a line and the two halves match up perfectly. Think of it like a mirror line. Let's look at some examples.

One Line of Symmetry

Multiple Lines of Symmetry

No Lines of Symmetry

My Notes on Line Symmetry:

A line of symmetry is a line that divides a figure into two halves.

We Do: Let's Find Lines of Symmetry

Together, let's find and count the lines of symmetry for each figure. How many does each one have?

Rectangle

Lines:

Regular Pentagon

Lines:

Parallelogram

Lines:

Key Idea:

A regular polygon with 'n' sides has lines of symmetry.

You Do: Draw the Lines of Symmetry

On your handout, draw all the lines of symmetry for each figure. Write down how many you find.

Equilateral Triangle

Count:

The Letter H

H

Count:

This Arrow

Count:

I Do: Understanding Point Symmetry

A figure has point symmetry if it looks the same when you turn it upside down (a 180° rotation). The point you rotate it around is the center of symmetry.

Has Point Symmetry

The letter 'S' rotated 180°

S

(Hover to see rotation)

No Point Symmetry

The letter 'F' rotated 180°

F

(Hover to see it doesn't match)

My Notes on Point Symmetry:

Point symmetry means a shape looks the same after a degree rotation.

We Do / You Do: Line, Point, Both, or Neither?

Let's classify these figures. Does the figure have line symmetry, point symmetry, both, or neither?

Figure Line Symmetry? Point Symmetry? Classification
+
A
F

Independent Practice

Work through the following problems. Start with Green and work your way up!

Level: Green

1. Draw the line(s) of symmetry for a heart shape.

2. Does the number 8 have point symmetry? Yes or No?

3. How many lines of symmetry does a regular octagon have?

Level: Yellow

4. Draw a quadrilateral that has exactly one line of symmetry and no point symmetry. What is its name?

5. The word NOON is written in capital letters. Does it have point symmetry, line symmetry, both, or neither?

Level: Red

6. Can a triangle have point symmetry? Explain your reasoning.

7. Create a company logo that has both point symmetry and at least two lines of symmetry. Sketch your logo below.

✅ Exit Ticket

Please complete the following questions on your own. This will show what you've learned today!

1. Draw all lines of symmetry on the figure below.

2. Does the letter 'N' have point symmetry? Explain why or why not.

3. Name a real-world object not mentioned in class that has line symmetry.