Constructions and Tilings

What is the term for a pattern made of identical shapes that fit together without gaps?

Which of these shapes is a quadrilateral that can easily tessellate a floor?

A student is given one side and two angles of a triangle. Which criterion should they use for construction?

Can a triangle be formed with angles $110^\circ, 40^\circ,$ and $30^\circ$?

In the RHS construction of $\triangle XYZ$ where $\angle Y = 90^\circ$, $YZ = 6\text{ cm}$, and the hypotenuse $XZ = 10\text{ cm}$, a student begins by drawing the segment $YZ$ and a perpendicular ray at $Y$. What radius must the student set on their compass to draw an arc from center $Z$ that will intersect the perpendicular ray to locate vertex $X$?

In $\triangle PQR$, a student is given the measurements $PQ = 6.5\text{ cm}$, $\angle P = 100^\circ$, and $\angle R = 35^\circ$. To construct this triangle using the ASA (Angle-Side-Angle) criterion specifically on the base $PQ$, what is the measure of the angle that the student must first calculate and then construct at vertex $Q$?

Which of the following side combinations can form an isosceles triangle?

While constructing a parallel line through a point $P$ using a transversal and alternate angles, if the arcs used to copy the angle have different radii, the lines will be:

If you construct a triangle with sides $8\text{ cm}, 15\text{ cm}, 17\text{ cm}$, what is the measure of the angle opposite the $17\text{ cm}$ side?

A regular polygon with interior angle $x$ can tile a plane if $360/x$ is:

Is it possible to tile a plane using a combination of regular octagons and squares?

What is the measure of each exterior angle of a regular hexagon?

Which of these figures is a 3-sided regular polygon?

In a tiling, can the shapes be of different colors?

A designer is creating a pattern by arranging regular pentagons. If three regular pentagons are placed edge-to-edge so that they meet at a single vertex, and each pentagon has an interior angle of $108^\circ$, what is the measure of the angular gap remaining at that vertex?

What is the sum of interior angles of a regular hexagon?

A semi-regular tiling uses squares and regular octagons. How many octagons and how many squares meet at each vertex?

What is the interior angle of a regular polygon if $5$ such polygons meet at a vertex and leave a $60^\circ$ gap?

A tiling is composed of regular hexagons. If each side of the hexagon is $a$, what is the distance between the centers of two adjacent hexagons?

If a vertex configuration is $n.n.n.n.n.n$, what is the value of $n$?