Mathematics
Grade 3
15 min
Line Symmetry
Line Symmetry
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1
Introduction & Learning Objectives
Learning Objectives
Define line symmetry in their own words.
Identify the line of symmetry in a given shape.
Determine if a shape is symmetrical or asymmetrical.
Draw one or more lines of symmetry on various geometric shapes.
Complete the other half of a symmetrical figure when given one half and a line of symmetry.
Sort shapes based on whether they have zero, one, or more than one line of symmetry.
Identify examples of line symmetry in real-world objects.
Have you ever folded a piece of paper in half to cut out a perfect heart? ❤️ Let's find out the math magic behind that!
In this lesson, we will explore line symmetry, which is like a mirror image in a shape. You will learn how to find special 'fold lines' that divide shapes into two exact matching halves....
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Key Concepts & Vocabulary
TermDefinitionExample
SymmetrySymmetry is when one half of an object is the exact mirror image of the other half.A butterfly is symmetrical because its left wing is a mirror image of its right wing.
Line of SymmetryAn imaginary line that divides a shape into two identical, matching halves. It's also called a 'mirror line' or a 'fold line'.The line you fold a piece of paper on to make a perfect heart is the line of symmetry.
Symmetrical ShapeA shape that has at least one line of symmetry.A square is a symmetrical shape because it has four lines of symmetry.
Asymmetrical ShapeA shape that has no lines of symmetry. You cannot fold it anywhere to make two matching halves.A drawing of a hand is asymmetrical.
Matching HalvesThe two equal parts of a shape that are on eit...
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Core Formulas
The Fold Test
A line is a line of symmetry if, when the shape is folded along that line, the two halves match up perfectly.
Use this test to check if a line you've drawn is a true line of symmetry. Imagine folding a paper shape along the line. If the edges don't line up, it's not a line of symmetry.
The Mirror Test
A line is a line of symmetry if, when a mirror is placed on the line, the reflection in the mirror completes the shape perfectly.
This is a great way to find lines of symmetry. Place a small craft mirror on a shape. If what you see in the mirror looks exactly like the other half of the shape, you've found a line of symmetry.
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Challenging
Which of these shapes has BOTH a vertical line of symmetry AND a horizontal line of symmetry?
A.An isosceles triangle
B.The capital letter T
C.rectangle
D.regular pentagon (5 sides)
Challenging
Which statement is TRUE about the lines of symmetry in a square and a rectangle (that is not a square)?
A.They both have 4 lines of symmetry.
B.The square has more lines of symmetry than the rectangle.
C.The rectangle has more lines of symmetry than the square.
D.Only the square has lines of symmetry.
Challenging
You are drawing a symmetrical shape. You draw the left half and the vertical line of symmetry. To draw the right half, every point on the right must be...
A.The same distance from the top as the matching point on the left.
B.The same distance from the line of symmetry as the matching point on the left.
C.Closer to the line of symmetry than the matching point on the left.
D.different shape from the matching point on the left.
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