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Group shapes based on their properties and find perfect balance with lines of symmetry.
What if you could find a 'magic line' that splits any object into two perfect mirror images? From the wings of a butterfly to the tiles on your floor, math is the secret to this perfect balance!
Triangles are like families; they come in different shapes, but they all have three sides and three angles. We name them by looking at their largest angle. A Right Triangle is the easiest to spot because it has one 'square' corner that measures exactly . An Acute Triangle is 'a-cute' little triangle where all three angles are smaller than . Finally, an Obtuse Triangle is the 'wide' one. It has one angle that is larger than , making it look like it is leaning back.
1. Look at a triangle. 2. Use the corner of a piece of paper to check the angles. 3. If the paper corner fits perfectly into one angle, it is . 4. This triangle is a Right Triangle.
Quick Check
What do we call a triangle where every angle is smaller than a right angle?
Answer
An Acute Triangle.
Have you ever looked in a mirror? Line Symmetry is just like that! A shape has line symmetry if you can draw an imaginary line through it and fold it so that both halves match perfectly. This line is called the Line of Symmetry. Think of the letter 'A': if you draw a line down the middle, the left side is a mirror image of the right side. If you fold a shape and the edges don't line up exactly, that line is not a line of symmetry.
1. Take a standard sheet of paper (a rectangle). 2. Fold it in half from top to bottom. The corners match! That is line. 3. Fold it in half from left to right. The corners match! That is lines. 4. Now, try to fold it from one corner to the opposite corner (diagonally). 5. Notice how the corners do NOT line up? This means a rectangle does not have diagonal symmetry. 6. Total lines of symmetry for a rectangle = .
Quick Check
If you fold a shape and the two halves do not match, does that fold represent a line of symmetry?
Answer
No, both halves must match perfectly.
Some shapes are symmetry superstars! A Regular Polygon (a shape where all sides and angles are equal) has as many lines of symmetry as it has sides. For example, a square has equal sides and lines of symmetry. A regular pentagon has . The ultimate winner is the circle. Because you can fold a circle through the center in any direction, it has an infinite number of lines of symmetry!
1. Look at a regular hexagon ( equal sides). 2. Draw lines connecting opposite corners (vertices). You will find lines. 3. Draw lines connecting the centers of opposite sides. You will find more lines. 4. Add them together: . 5. A regular hexagon has lines of symmetry!
A triangle has angles measuring , , and . What type of triangle is it?
How many lines of symmetry does a square have?
A circle has exactly 4 lines of symmetry.
Review Tomorrow
In 24 hours, try to draw one triangle of each type (Acute, Right, Obtuse) and label them from memory.
Practice Activity
Go on a 'Symmetry Scavenger Hunt'! Find 3 items in your home that have at least one line of symmetry and 1 item that has zero symmetry.