IM 1
Investigation 4.1.3A
Name
Line Symmetry: A shape has Line Symmetry (or Reflection Symmetry) if there is a line that can be drawn so
that the shape is a mirror image on both sides of the line.
Vertical Line of Symmetry: You can see the
vertical line drawn in the AAA sign below shows
that the two halves of the picture are mirror
images.
Horizontal Line of Symmetry: You can see the
horizontal line drawn on the butterfly below
shows that the two halves of the picture are
mirror images.
1) Which of the following pictures have Line Symmetry? Draw in all possible lines of symmetry. Be careful
there can also be Diagonal Lines of Symmetry, and some of these shapes have multiple lines of symmetry.
2)
Which of the types of quadrilaterals have reflection symmetry? Fill in the table with Yes or No for each
shape. Draw in the reflection line(s) for each shape, count the number of different lines of symmetry,
and record the number in the table.
3) Circle the letters of the alphabet, when written with capitol letters, that have vertical line symmetry?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
4) Which of the letters of the alphabet, when written with capitol letters, have horizontal line symmetry?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
5) Use the graph of the parallelogram shown below to complete the following steps.
a) Fill in the coordinates of the original image in the table below.
b) Reflect the points over the X-axis and redraw the shape.
c) What kind of symmetry line is the x-axis?
d) Fill in the coordinates of the reflected image in the table.
6) Use the graph of the parallelogram shown below to complete the following steps.
a) Fill in the coordinates of the original image in the table below.
b) Reflect the points over the Y-axis and redraw the shape.
c) What kind of symmetry line is the y-axis?
d) Fill in the coordinates of the reflected image in the table.
7) A regular polygon has all sides equal and all angles equal. How many lines of symmetry does each of the
following regular polygons have? Name the shape and draw in all the lines of symmetry.
8) The following shape is a rectangle with measurements AB = 12cm, BC = 30cm, BE = 16.2CM,
∠EAD = 35°, and ∠AEB = 70°
Calculate the length of each of the missing segments.
CD =
AD =
AE =
CE =
AC =
DE =
BD =
Calculate the length of each of the missing angles.
∠A =
∠EAB =
∠B =
∠EBA =
∠EBC =
∠C =
∠DCE =
∠BCE =
∠BEC =
∠CED =
∠DEA =
9) The following shape is a parallelogram with measurements AB = 25in, AD = 14in, AE = 12in, BE = 16in,
∠B = 75°, ∠EAB = 35°, and ∠EBC = 45°.
Calculate the length of each of the missing segments.
BC =
CD =
AC =
CE =
DE =
BD =
Calculate the length of each of the missing angles.
∠A =
∠C =
∠D =
∠EAD =
∠EBA =
AEB =
∠EDA =
∠DEA =
∠EDC =
∠BCE =
∠DCE =
∠CED =