Section 1
📘 Symmetry
New Concept
We call this kind of balance reflective symmetry, or just symmetry.
What’s next
Next, you'll identify lines of symmetry and check for rotational symmetry in various shapes and letters.
In this Grade 4 Saxon Math lesson from Chapter 8, students learn to identify and draw lines of reflective symmetry in polygons, letters, and other figures, and distinguish figures that have rotational symmetry from those that do not. Students use a mirror as a hands-on tool to explore how a line of symmetry divides a figure into two mirror-image halves, and they examine how figures like squares and regular polygons rotate to match their original positions at specific degree intervals. The lesson builds geometric reasoning skills through classifying shapes, uppercase letters, and real-world examples by their symmetry properties.
Section 1
📘 Symmetry
We call this kind of balance reflective symmetry, or just symmetry.
Next, you'll identify lines of symmetry and check for rotational symmetry in various shapes and letters.
Section 2
Line of symmetry
A line of symmetry is a line that divides a figure into two halves that are mirror images of each other. If a figure is folded along a line of symmetry, the two halves of the figure will match exactly.
An isosceles triangle has one vertical line of symmetry. A square has four lines of symmetry: one vertical, one horizontal, and two diagonal. The letter 'A' has one vertical line of symmetry, while the letter 'R' has none.
Imagine you have a piece of paper cut into a shape, like a heart or a star. If you can fold it perfectly in half so that the edges line up, that fold line is a line of symmetry! It's the magic dividing line where one side is the perfect reflection of the other side.
Section 3
Rotational symmetry
A figure has rotational symmetry if it matches its original position as it is rotated less than a full turn () around a central point. For example, a square matches itself every quarter turn ().
A square has rotational symmetry and matches itself every quarter turn (). The letter 'H' has rotational symmetry, as it looks the same after a half turn (). A regular pentagon matches its original position every one-fifth of a turn ().
Think of a shape on a spinner, like a pinwheel or the letter 'S'. If you can spin it partway around and it looks exactly the same as when it started, it has rotational symmetry! It’s all about looking identical after a partial spin, before it goes all the way around back to the beginning.
Section 4
Symmetry in letters
Many uppercase letters of the alphabet have symmetry. Some have reflective symmetry (like 'A', 'T', 'M'), some have rotational symmetry (like 'S', 'N', 'Z'), and some special letters (like 'H', 'I', 'O', 'X') have both types of symmetry.
The letter 'T' has one vertical line of symmetry but no rotational symmetry. The letter 'Z' has rotational symmetry () but no lines of symmetry. The letter 'X' has two lines of symmetry and rotational symmetry.
The alphabet is like a secret club for shapes! Some letters, like 'A' and 'V', can be split perfectly by a mirror line. Others, like 'N' and 'Z', can be spun halfway around and look the same. And then there are the superstars like 'H' and 'O' that can do both! It's a hidden superpower.
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Section 1
📘 Symmetry
We call this kind of balance reflective symmetry, or just symmetry.
Next, you'll identify lines of symmetry and check for rotational symmetry in various shapes and letters.
Section 2
Line of symmetry
A line of symmetry is a line that divides a figure into two halves that are mirror images of each other. If a figure is folded along a line of symmetry, the two halves of the figure will match exactly.
An isosceles triangle has one vertical line of symmetry. A square has four lines of symmetry: one vertical, one horizontal, and two diagonal. The letter 'A' has one vertical line of symmetry, while the letter 'R' has none.
Imagine you have a piece of paper cut into a shape, like a heart or a star. If you can fold it perfectly in half so that the edges line up, that fold line is a line of symmetry! It's the magic dividing line where one side is the perfect reflection of the other side.
Section 3
Rotational symmetry
A figure has rotational symmetry if it matches its original position as it is rotated less than a full turn () around a central point. For example, a square matches itself every quarter turn ().
A square has rotational symmetry and matches itself every quarter turn (). The letter 'H' has rotational symmetry, as it looks the same after a half turn (). A regular pentagon matches its original position every one-fifth of a turn ().
Think of a shape on a spinner, like a pinwheel or the letter 'S'. If you can spin it partway around and it looks exactly the same as when it started, it has rotational symmetry! It’s all about looking identical after a partial spin, before it goes all the way around back to the beginning.
Section 4
Symmetry in letters
Many uppercase letters of the alphabet have symmetry. Some have reflective symmetry (like 'A', 'T', 'M'), some have rotational symmetry (like 'S', 'N', 'Z'), and some special letters (like 'H', 'I', 'O', 'X') have both types of symmetry.
The letter 'T' has one vertical line of symmetry but no rotational symmetry. The letter 'Z' has rotational symmetry () but no lines of symmetry. The letter 'X' has two lines of symmetry and rotational symmetry.
The alphabet is like a secret club for shapes! Some letters, like 'A' and 'V', can be split perfectly by a mirror line. Others, like 'N' and 'Z', can be spun halfway around and look the same. And then there are the superstars like 'H' and 'O' that can do both! It's a hidden superpower.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter