1. E11 make generalizations about the rotational symmetry property of squares and rectangles and apply them.

2. Let’s Review: What are the properties of squares that you already know? A square is a quadrilateral. A square is a quadrilateral. A square has four congruent side lengths. A square has four congruent side lengths. A square has four equal angles. A square has four equal angles. A square is a special type of rhombus. A square is a special type of rhombus. A square is a parallelogram. A square is a parallelogram. Each angle in a square measures 90 degrees. Each angle in a square measures 90 degrees. The diagonals of a square are equal in length; bisect each other; intersect to form four right angles and combined with the previous properties this means they are perpendicular-bisectors of each other; are bisectors of the vertex angles of the square, thus forming 45 degree angles; and form four congruent isosceles right triangles The diagonals of a square are equal in length; bisect each other; intersect to form four right angles and combined with the previous properties this means they are perpendicular-bisectors of each other; are bisectors of the vertex angles of the square, thus forming 45 degree angles; and form four congruent isosceles right triangles

3. Now let’s investigate another property of squares: Use a square from the pattern blocks, and mark one of its vertices with a chalk dot. Use a square from the pattern blocks, and mark one of its vertices with a chalk dot. Next, carefully trace the block to make a square on a sheet of paper. Next, carefully trace the block to make a square on a sheet of paper. With the square block placed inside its picture, rotate it clockwise with the centre of rotation being the centre of the square (intersection point of its two diagonals) until it perfectly matches its picture again. With the square block placed inside its picture, rotate it clockwise with the centre of rotation being the centre of the square (intersection point of its two diagonals) until it perfectly matches its picture again. Notice that the marked vertex is at the next corner. Notice that the marked vertex is at the next corner. Repeat this rotation. How many times does the square appear in four identical positions during one complete 360- degree rotation? Repeat this rotation. How many times does the square appear in four identical positions during one complete 360- degree rotation? The answer is 4, and the square is said to have rotational symmetry of order 4. The answer is 4, and the square is said to have rotational symmetry of order 4.

4. Rotational Symmetry of a Square

5. Let’s Review: What are the properties of rectangles that you already know? A rectangle is a quadrilateral. A rectangle is a quadrilateral. A rectangle has four equal angles. A rectangle has four equal angles. A rectangle is a special type of parallelogram with all 90- degree angles. A rectangle is a special type of parallelogram with all 90- degree angles. The diagonals of a rectangle are are equal in length; bisect each other; form two pairs of equal opposite angles at the point of intersection; form two angles at each vertex of the rectangle that sum to 90 degrees and have the same measures as the two angles at the other vertices; and The diagonals of a rectangle are are equal in length; bisect each other; form two pairs of equal opposite angles at the point of intersection; form two angles at each vertex of the rectangle that sum to 90 degrees and have the same measures as the two angles at the other vertices; and form two pairs of congruent isosceles triangles

6. Now let’s investigate another property of rectangles: Make a rectangle from hard paper, and mark one of its vertices with a chalk dot. Make a rectangle from hard paper, and mark one of its vertices with a chalk dot. Next, carefully trace the rectangle to make a second rectangle on a sheet of paper. Next, carefully trace the rectangle to make a second rectangle on a sheet of paper. With the rectangle block placed inside its picture, rotate it clockwise with the centre of rotation being the centre of the rectangle (intersection point of its two diagonals) until it perfectly matches its picture again. With the rectangle block placed inside its picture, rotate it clockwise with the centre of rotation being the centre of the rectangle (intersection point of its two diagonals) until it perfectly matches its picture again. Notice that the marked vertex is at the next corner. Notice that the marked vertex is at the next corner. Repeat this rotation. How many times does the rectangle appear in four identical positions during one complete 360- degree rotation? Repeat this rotation. How many times does the rectangle appear in four identical positions during one complete 360- degree rotation? The answer is 2, and the rectangle is said to have rotational symmetry of order 4. The answer is 2, and the rectangle is said to have rotational symmetry of order 4.

7. Rotational Symmetry of a Rectangle

8. http://regentsprep.org/Regents/math/quad/LQuad.htm Meet Some of the Members of the Quadrilateral Family

9. Student Activities: E11.1 Investigate to find out if a square is the only quadrilateral with rotational symmetry of order 4. E11.1 Investigate to find out if a square is the only quadrilateral with rotational symmetry of order 4. E11.2 Investigate what other quadrilaterals besides rectangles have rotational symmetry of order 2. E11.2 Investigate what other quadrilaterals besides rectangles have rotational symmetry of order 2. Which ones also have two lines of reflective symmetry? Which ones also have two lines of reflective symmetry?