In this Grade 7 Saxon Math Course 2 lesson, students explore reflective symmetry and rotational symmetry in two-dimensional figures, learning to identify lines of symmetry and determine the order of rotational symmetry for polygons and letters. Students practice drawing lines of symmetry for regular polygons such as squares and triangles, and analyze figures on a coordinate plane where the y-axis serves as a line of symmetry. The lesson builds spatial reasoning skills through hands-on cutting activities and connects symmetry concepts to real-world shapes and objects.
Section 1
📘 Symmetry
Symmetry is when a shape remains unchanged after being flipped, slid, or turned. It is a core idea in geometry that describes balance and proportion.
Next, you’ll master the two key types of symmetry. We’ll practice identifying them in figures and even use them to solve puzzles on a graph.
Section 2
Reflective symmetry
A two-dimensional figure has reflective symmetry or line symmetry if it can be divided in half so that the halves are mirror images of each other. The dividing line is a line of symmetry.
A square is super symmetric, with four lines of symmetry: one vertical, one horizontal, and two diagonals.
A rectangle only has two lines of symmetry; its diagonals are not lines of symmetry because the halves don't match when folded.
If a triangle symmetric about the y-axis has vertices at and , its third vertex must be at $(-3, 4).
Think of it as a perfect fold! If you can fold a shape along a line so that both halves match up exactly, you've found a line of symmetry. It's like looking into a mirror where one half reflects to become the other.
Section 3
Rotational symmetry
A figure has rotational symmetry if it re-appears in its original position more than once in a full turn.
The letter 'S' has rotational symmetry because it looks the same after a half-turn ().
A regular triangle has rotational symmetry because it looks identical after being rotated by and .
A square reappears in its original position after turns of , , and .
Imagine spinning a shape around its center. If it looks exactly the same before you've completed a full rotation, it has rotational symmetry. It's like a fidget spinner that looks identical with each partial spin!
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Section 1
📘 Symmetry
Symmetry is when a shape remains unchanged after being flipped, slid, or turned. It is a core idea in geometry that describes balance and proportion.
Next, you’ll master the two key types of symmetry. We’ll practice identifying them in figures and even use them to solve puzzles on a graph.
Section 2
Reflective symmetry
A two-dimensional figure has reflective symmetry or line symmetry if it can be divided in half so that the halves are mirror images of each other. The dividing line is a line of symmetry.
A square is super symmetric, with four lines of symmetry: one vertical, one horizontal, and two diagonals.
A rectangle only has two lines of symmetry; its diagonals are not lines of symmetry because the halves don't match when folded.
If a triangle symmetric about the y-axis has vertices at and , its third vertex must be at $(-3, 4).
Think of it as a perfect fold! If you can fold a shape along a line so that both halves match up exactly, you've found a line of symmetry. It's like looking into a mirror where one half reflects to become the other.
Section 3
Rotational symmetry
A figure has rotational symmetry if it re-appears in its original position more than once in a full turn.
The letter 'S' has rotational symmetry because it looks the same after a half-turn ().
A regular triangle has rotational symmetry because it looks identical after being rotated by and .
A square reappears in its original position after turns of , , and .
Imagine spinning a shape around its center. If it looks exactly the same before you've completed a full rotation, it has rotational symmetry. It's like a fidget spinner that looks identical with each partial spin!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter