Lines and shapes

Advanced Math 4 · Unit 16 · lines-symmetry-quadrilaterals · Teacher edition

lines-symmetry-quadrilaterals

Name ______________________________Date ______________

1.
How many lines of symmetry does a square have?
Answer: ______________
2.
A rectangle is $8$ cm long and $6$ cm wide. A line of symmetry is drawn parallel to the $6$ cm sides, cutting the rectangle into two equal pieces. What is the perimeter of one piece, in cm?
Answer: ______________
3.
Which statement is true?
1. (A)
  Every rectangle is a square.
2. (B)
  A square is not a rectangle, because all four of its sides are equal.
3. (C)
  A rectangle has exactly two right angles.
4. (D)
  Every square is a rectangle.

Answer key — Lines and shapes

1.
4lines-symmetry-quadrilaterals-01
Two lines join the midpoints of opposite sides and two are the diagonals: $\mathbf{4}$ lines of symmetry. (A rectangle that is not a square has only the first two; its diagonals do not work.)
2.
20lines-symmetry-quadrilaterals-02
The fold line cuts the $8$ cm sides into $4$ cm halves, so each piece is $6$ cm by $4$ cm. Perimeter $= 2(6 + 4) = \mathbf{20}$ cm. (Halving the original perimeter of $28$ gives $14$ , which is wrong: the cut adds two new $6$ cm edges.)
3.
(D)
Every square is a rectangle.
lines-symmetry-quadrilaterals-03
A square has four right angles, so it meets the definition of a rectangle: every square is a rectangle. (Not every rectangle is a square — an $8$ by $6$ one is not; having equal sides is an extra property, not a reason to stop being a rectangle; every rectangle has four right angles, not two.)