Shape and Space

How many lines of symmetry does an equilateral triangle have?

What is the common name for a quadrilateral with two pairs of parallel sides?

Which of these describes a square but NOT every rhombus?

A triangle has angles of $30^\circ$, $120^\circ$, and $30^\circ$. How is it classified by its angles?

Look at the triangle in the coordinate plane. What are its properties?

In the quadrilateral $ABCD$, sides $AB=BC=CD=DA$. If the diagonals $AC$ and $BD$ are NOT equal, the shape is a:

If an isosceles triangle has a vertex angle of $100^\circ$, what is the measure of one of its base angles?

A quadrilateral has two pairs of parallel sides. All four sides are equal in length, and all four angles are $90^\circ$. Which is the most specific name for this shape?

A triangle has one angle that is $110^\circ$. What must be true about the other two angles, and how is the triangle classified?

Which of the following statements about quadrilaterals is always true?

Which of the following shapes has the highest number of faces?

What is the shape of the base of a cone?

How many vertices does a decagonal (10-sided) prism have?

The point where the triangular faces of a pyramid meet at the top is called the...?

A certain prism has a total of $18$ vertices. How many faces does this prism have in total?

A model is made by joining a square-based pyramid to a cube. The base of the pyramid is exactly the same size as one face of the cube and is placed directly on top of it so that the edges and vertices align perfectly. How many vertices does this new combined shape have?

If a solid cylinder is sliced vertically (perpendicular to the bases) such that the cut passes through the centers of both circular bases, what 2D shape is formed by the cross-section?

If you have 4 cubes and arrange them in a single straight row, touching face-to-face, how many faces are visible on the outside of the resulting shape?

How many vertices are in a decagonal pyramid?

A 3D shape is formed by 4 triangles. What is the total number of vertices?

If you rotate an object by $\frac{1}{8}$ of a full turn, how many degrees have you rotated it?

Which shape has the highest order of rotational symmetry?

How many lines of symmetry does a regular decagon (10 sides) have?

If you rotate a shape $180^\circ$ counter-clockwise, it is the same as a ________ clockwise.

A square floor tile is divided into four equal smaller square sections. If the top-left and bottom-right sections are shaded, and the top-right and bottom-left sections are left white, what is the order of rotational symmetry for this tile's design around its center?

If a shape is rotated $450^\circ$ clockwise, this is equivalent to which simple rotation?

How many lines of symmetry does a regular 12-sided polygon have?

A $4 \times 4$ grid has its squares identified by coordinates $(x, y)$, where $x$ is the column number (1 to 4) and $y$ is the row number (1 to 4). If the squares at $(1, 4)$ and $(4, 1)$ are already shaded, which two additional squares must be shaded to ensure the entire grid has rotational symmetry of order 4?

A shape has a vertex located at the coordinate $(4, 4)$. The shape is first reflected across the horizontal line $y = 1$ and then rotated $180^\circ$ about the point $(3, 1)$. What are the final coordinates of that vertex?

A square with vertices at $A(1, 1)$, $B(1, 3)$, $C(3, 3)$, and $D(3, 1)$ is rotated $90^\circ$ counter-clockwise. After the rotation, the new position of vertex $A$ is at $(-1, 1)$ and the new position of vertex $B$ is at $(-3, 1)$. What are the coordinates of the center point around which the square was rotated?

Which of these points has a $y$-coordinate that is double its $x$-coordinate?

A point is 2 units from the $y$-axis and 5 units from the $x$-axis. What are its coordinates?

What is the $x$-coordinate of the square's top-right vertex?

Find the coordinates of the vertices of the triangle shown.

Points $(2, 1), (4, 1), (4, 4)$, and $(2, 4)$ form a shape. What is its area?

Triangle $PQR$ has vertices $P(1, 1)$, $Q(5, 1)$, and $R(3, 4)$. What is the height of the triangle from base $PQ$?

A line segment connects $(1, 1)$ to $(5, 5)$. Which of the following points lies on this segment?

A bird flies from $(3, 3)$ to $(3, 7)$, then to $(9, 7)$, and finally back to $(3, 3)$. What is the perimeter of the triangle formed by the bird's flight path? (Note: The distance from $(3, 7)$ to $(9, 7)$ is 6 units, and the distance from $(9, 7)$ back to $(3, 3)$ is roughly 7.2 units).

A park is shaped like a right-angled triangle. Its vertices are at $(2, 2)$, $(9, 2)$, and $(2, 9)$. What is the area of the park in square units?

An artist is drawing a line that represents a hill. The line passes through $(0, 0)$, $(2, 4)$, and $(4, 8)$. If the artist continues this linear pattern, what will be the $y$-coordinate when the $x$-coordinate is $5$?

Which of these looks like a tessellation in a kitchen?

If a pattern of shapes has overlaps, is it a tessellation?

Which of these shapes can be found in a tessellation?

Which of the following describes a translation in a tessellation?

If you reflect a right-angled triangle across its longest side (hypotenuse) and then tessellate the result, you are effectively tessellating with:

In a tessellation of regular hexagons, what is the angle of each corner where they meet?

What is the name for a tiling that covers the plane but never repeats exactly, like Penrose tiles?

Which of these is the correct interior angle for a regular 15-gon?

If you take a square and perform a 'midpoint stretch' on two opposite sides, resulting in a hexagon with two long parallel sides and four shorter sides, can it still tessellate?

A tessellation is made of congruent rhombi with angles of $60^\circ$ and $120^\circ$. How many rhombi meet at a vertex composed only of $60^\circ$ angles?