Transformations and Patterns in Geometry

A square is turned 90° around its center point. Which transformation best describes this movement?

• Translation

• Rotation

• Reflection

• Dilation

A triangle is shifted 6 units to the right on a coordinate plane without changing its size or shape. What transformation is applied?

• Translation

• Reflection

• Rotation

• Dilation

A kite pattern is created where each kite is flipped across a diagonal line to complete the design. Which transformation is used?

• Translation

• Reflection

• Rotation

• Dilation

Which of the following polygons cannot tessellate the plane by itself?

• Equilateral triangle

• Square

• Regular pentagon

• Regular hexagon

A tessellation is made with squares and equilateral triangles. Which type of tessellation is this?

• Regular tessellation

• Semi-regular tessellation

• Irregular tessellation

• Non-periodic tessellation

Which transformation combines a reflection followed by a translation?

• Rotation

• Glide reflection

• Dilation

• Shear

In a frieze pattern, a motif is copied by sliding it repeatedly along a horizontal line without rotation or reflection. What is this transformation?

• Translation

• Reflection

• Rotation

• Glide reflection

The Parthenon in Greece is often said to reflect which mathematical ratio in its design?

• 1:2

• 2:3

• Golden ratio

• Fibonacci ratio

Which of the following natural examples most clearly illustrates the Fibonacci sequence?

• Stripes on a zebra

• Arrangement of sunflower seeds

• Length of a river

• Shape of a cube

Which best explains why Fibonacci numbers appear in sunflower seed arrangements?

• They prevent overlap and allow efficient packing.

• They form exact squares in every spiral.

• They are required by plant genetics.

• They occur only by random chance.