Final Answer:
The correct shapes and their corresponding rotational symmetries are:
a.) Square - 5 lines of symmetry and order 5 rotational symmetry b.) Isosceles triangle - no lines of symmetry and order 1 rotational symmetry c.) Rectangle - one line of symmetry and order 1 rotational symmetry d.) Regular octagon - 8 lines of symmetry and order 8 rotational symmetry e.) Scalene triangle - no lines of symmetry and order 1 rotational symmetry f.) Parallelogram - four lines of symmetry and order 4 rotational symmetry g.) Regular pentagon - two lines of symmetry and order 2 rotational symmetry
Step-by-step explanation:
To determine the correct shape and rotational symmetry for each description, we need to analyze the given information carefully.
a.) “I have five lines of symmetry and order 5 rotational symmetry.” - This description fits a square perfectly. A square has five lines of symmetry (horizontally, vertically, and along the diagonals) and order 5 rotational symmetry, which means it looks the same after rotating it 5 times.
b.) “I have no lines of symmetry and order 2 rotational symmetry.” - This description fits an isosceles triangle perfectly. An isosceles triangle has no lines of symmetry, but it has order 2 rotational symmetry, which means it looks the same after rotating it 180 degrees.
c.) “I have one line of symmetry and order 1 rotational symmetry.” - This description fits a rectangle perfectly. A rectangle has one line of symmetry (the vertical line in the middle) and order 1 rotational symmetry, which means it looks the same after rotating it 180 degrees.
d.) “I have eight lines of symmetry and order 8 rotational symmetry.” - This description fits a regular octagon perfectly. A regular octagon has eight lines of symmetry (all the sides and the diagonals) and order 8 rotational symmetry, which means it looks the same after rotating it 8 times.
e.) “I have no lines of symmetry and order 1 rotational symmetry.” - This description fits a scalene triangle perfectly. A scalene triangle has no lines of symmetry, but it has order 1 rotational symmetry, which means it looks the same after rotating it 180 degrees.
f.) “I have four lines of symmetry and order 4 rotational symmetry.” - This description fits a parallelogram perfectly. A parallelogram has four lines of symmetry (the sides and the diagonals) and order 4 rotational symmetry, which means it looks the same after rotating it 4 times.
g.) “I have two lines of symmetry and order 2 rotational symmetry.” - This description fits a regular pentagon perfectly. A regular pentagon has two lines of symmetry (the sides) and order 2 rotational symmetry, which means it looks the same after rotating it 2 times.
In conclusion, the correct shapes and their corresponding rotational symmetries are:
a.) Square - 5 lines of symmetry and order 5 rotational symmetry b.) Isosceles triangle - no lines of symmetry and order 1 rotational symmetry c.) Rectangle - one line of symmetry and order 1 rotational symmetry d.) Regular octagon - 8 lines of symmetry and order 8 rotational symmetry e.) Scalene triangle - no lines of symmetry and order 1 rotational symmetry f.) Parallelogram - four lines of symmetry and order 4 rotational symmetry g.) Regular pentagon - two lines of symmetry and order 2 rotational symmetry