Line Symmetry
Warm-up
Hold a mirror along the vertical axis of a square. Do the two halves match? (Yes.) Move the mirror to a diagonal. Still match? (Yes.) How many positions work? (4.) Now a rectangle: how many work? (2, not 4, because the diagonals do not give symmetry unless it is a square.)
Explore
Symmetry investigation: each student has 6 regular polygon cutouts (triangle through hexagon). Find all lines of symmetry for each by folding. Record counts. Notice: equilateral triangle 3, square 4, regular pentagon 5, regular hexagon 6. Write the pattern in words.
Consolidate
Practice
Students find all lines of symmetry for 8 shapes (recording with drawings), create a 4-fold symmetric design using paper folding, and identify symmetry in 3 First Peoples art images. Exit ticket: how many lines of symmetry does a regular pentagon have?
Exit ticket
Students find all lines of symmetry for 8 shapes (recording with drawings), create a 4-fold symmetric design using paper folding, and identify symmetry in 3 First Peoples art images. Exit ticket: how many lines of symmetry does a regular pentagon have?
A regular n-gon has n lines of symmetry. An octagon has 8 sides, so 8 lines of symmetry. (4 through opposite vertices + 4 through midpoints of opposite sides.)
No. Fold a rectangle along a diagonal: the two triangles overlap but the remaining corners do not align. The rectangle has 2 lines of symmetry (horizontal and vertical through the centre), not 4.