Shape and Space

If you follow a path that turns exactly $180^\circ$, what kind of angle have you made?

What do you call an angle that looks like the letter 'V'?

What is the total number of degrees in three right angles combined?

Which angle measurement is equivalent to exactly two right angles?

If an angle is $x$ and its supplement is $150^\circ$, what is $x$?

If you turn through two right angles and one acute angle of $30^\circ$, what is the total angle?

How many degrees are between the hands of a clock at 9:00 (smaller angle)?

Three angles on a line are in the ratio $1:2:3$. What is the reflex angle of the largest angle?

Which of the following describes an angle that is $5/4$ of a straight angle?

An angle is $x$. Its supplement is $4x$. What is the complement of $x$?

Which of the following describes the angles that are non-adjacent and share a vertex when two lines intersect?

Calculate the supplement of $2^\circ$.

Calculate the complement of $32^\circ$.

Two lines intersect. One angle is $73^\circ$. What is the measure of the vertically opposite angle?

The sum of an angle's complement and its supplement is $160^\circ$. What is the measure of the angle?

An angle is $15^\circ$ more than half of its complement. Find the measure of the angle.

The supplement of an angle $x$ is $5x$. Find the value of $x$.

Three lines intersect at a point. Let $a$ and $b$ be vertically opposite angles. If $a + b = 100^\circ$, find the measure of the supplement of $a$.

Angles $x$ and $y$ are complementary. Angles $y$ and $z$ are supplementary. If $z = 3x$, find the measure of angle $y$.

The supplement of an angle $x$ is $40^\circ$ more than twice the complement of $x$. Find the value of $x$.

The three angles of a triangle are $x, x$, and $40^\circ$. What is the value of $x$?

If one angle in a triangle is $92^\circ$, the triangle is definitely:

Which triangle will always have three equal angles of $60^\circ$?

If a triangle has sides of $4\text{ cm}, 5\text{ cm}$, and $6\text{ cm}$, its perimeter is:

The exterior angle at vertex $D$ of $\triangle DEF$ is $135^\circ$. If the two non-adjacent interior angles (at vertices $E$ and $F$) are in a ratio of $4:5$, what is the measure of the larger of these two interior angles?

A triangle has exactly one line of symmetry. If one of the angles in this triangle measures $112^\circ$, what is the measure of each of the remaining two angles?

In $\triangle ABC$, the side lengths are $AB = 8 \text{ cm}$, $BC = 6 \text{ cm}$, and $CA = 11 \text{ cm}$. Which of the following lists the interior angles in order from largest to smallest?

If the ratio of the exterior angles of a triangle is $4:5:6$, what is the measure of the smallest interior angle of the triangle?

A triangle has sides $x$, $x+1$, and $x+2$. If the perimeter is $18$, what is the classification of the triangle?

If an equilateral triangle and a regular hexagon share the same perimeter $P$, what is the ratio of the side of the triangle to the side of the hexagon?

A rectangle with four equal sides is a...?

How many pairs of equal sides does a kite have?

Which quadrilateral is formed by two congruent isosceles triangles joined at their bases?

Which shape has a rotational symmetry of order 2 but NO lines of symmetry?

A quadrilateral has exactly two lines of symmetry, and both of these lines connect the midpoints of opposite sides. What is the measure of each interior angle of this shape?

A quadrilateral with exactly two pairs of equal sides is definitely which of these?

What is the maximum number of acute angles a convex quadrilateral can have?

Which of these is the most specific name for a quadrilateral with 2 pairs of parallel sides and 4 equal sides?

Which quadrilateral has the property that exactly one diagonal is bisected by the other?

If the sum of two opposite angles of a quadrilateral is $180^{\circ}$, it must be:

Which 3D shape is defined by having $6$ faces, $8$ vertices, and $12$ edges?

Determine the number of edges on a pentagonal pyramid.

A heptagonal pyramid has how many vertices?

How many vertices are on a heptagonal prism?

A prism has exactly 18 edges and a pyramid also has exactly 18 edges. What is the total number of vertices these two shapes have combined?

How many faces are there in a dodecagonal (12-sided) pyramid?

Which net consists of one square and four triangles?

An $n$-gonal pyramid is placed on top of an $n$-gonal prism so that their bases coincide. How many vertices does the resulting solid have?

A solid shape has $V$ vertices, $F$ faces, and $E$ edges. If it is a heptagonal prism, calculate $E - (V + F)$.

How many edges meet at each vertex of a regular pentagonal prism?

How many triangles are in the net of a pentagonal pyramid?

A net consisting of $2$ decagons and $10$ rectangles forms a:

How many rectangles are in the net of a nonagonal prism?

If a net has $1$ square base and $4$ isosceles triangles, it is the net of a:

A net of a rectangular prism has dimensions such that all faces are rectangles. If the rectangles are $2 \times 3, 2 \times 5,$ and $3 \times 5$ (two of each), what is the total surface area?

If a 3D shape has $n$ faces, how many faces does its net have?

What is the shape of the side faces in the net of any regular prism?

If you have a net that forms a cube, and you move one of the squares to an adjacent edge, which of the following is true?

In a net for a cylinder, if the circumference of the base is $20\pi \text{ cm}$, what is the length of the rectangle in the net?

A net is composed of 4 triangles and 1 square. If the net is folded into a pyramid, and the area of the square is $16 \text{ cm}^2$ and each triangle has an area of $10 \text{ cm}^2$, what is the total surface area?

How many lines of symmetry does the capital letter $L$ have?

How many lines of symmetry does the capital letter $X$ have?

How many lines of symmetry does a right-angled isosceles triangle have?

How many lines of symmetry does a regular dodecagon (12 sides) have?

A pattern has an order of rotational symmetry of 8. If the pattern is rotated clockwise from $0^\circ$ up to and including $180^\circ$, how many times will it match its original starting position? (Do not count the starting position at $0^\circ$).

A shape is formed by removing a small square from one corner of a larger square, creating an L-shaped polygon with two arms of equal length and width. How many lines of symmetry does this polygon have?

How many lines of symmetry does the capital letter $F$ have?

If a shape is reflected across the $x$-axis and then the image is reflected across the $x$-axis again, what is the result?

A shape has order of rotational symmetry 10. What is the smallest angle greater than $0^{\circ}$ that maps the shape onto itself?

An equilateral triangle has its vertices at $(0, 2\sqrt{3}), (-2, 0),$ and $(2, 0)$. Which of the following is a line of symmetry for this triangle?

If point $S(1, 2)$ moves to $S'(1, -2)$, what transformation occurred?

Which transformation would you use to describe the motion of a drawer being pulled out?

A point at $(-6, 0)$ is reflected over the $y$-axis. Where is it now?

If you translate point $(x, y)$ by $a$ units horizontally and $b$ units vertically, the new point is:

Point $(2, 3)$ is reflected across the $x$-axis and then translated $1$ unit up. What is the final coordinate?

The point $(-7, 0)$ is translated $7$ units to the right. What is its new location?

If you reflect $(8, 8)$ across the $x$-axis twice, where does the point end up?

Point $K(0, 4)$ is rotated $180^\circ$ about the origin, then reflected across $y = 1$. What is the final image?

A point is at $(5, 5)$. It is translated by $\begin{pmatrix} -10 \\ -10 \end{pmatrix}$ and then reflected across the line $y = -x$. Where does it land?

Reflect point $J(3, -1)$ across the line $y = x$. Then rotate $90^\circ$ CW about the origin. What is the result?

What is the measurement of the angle formed by a straight line?

If an angle is $179^{\circ}$, it is classified as:

How many degrees are in two-thirds of a right angle?

A right angle is divided into two parts. If one part is $25^{\circ}$, what is the other part?

If a rotation of $540^{\circ}$ is made, how many full turns and what additional angle has been covered?

An angle $x$ is such that its supplement is 3 times its complement. Find $x$.

Two lines $L1$ and $L2$ are parallel. $L3$ is a transversal. If a pair of co-interior angles are $2x$ and $3x$, find the value of $x$.

If a line $L$ intersects two parallel lines $M$ and $N$, and one interior angle is $x^{\circ}$, what is the sum of that angle and its corresponding angle?

If the interior angle of a regular polygon is five times its exterior angle, how many sides does it have?

In an equilateral triangle, if a line is drawn from one vertex to the midpoint of the opposite side, what two angles are formed at that vertex?

Every square is also a type of:

How many pairs of parallel sides does a regular hexagon have?

A quadrilateral with four equal sides is always a:

What is the name of a polygon with 9 vertices?

A triangle has two sides of equal length and one interior angle that measures $110^\circ$. Classify this triangle by both its side lengths and its angle measures.

In a regular polygon, each interior angle measures exactly twice as much as each exterior angle. What is the name of this polygon?

A polygon has 6 sides. If 5 of its interior angles sum to $600^\circ$, what is the measure of the sixth angle?

A hexagon has three interior angles of $100^{\circ}$ each. If the other three angles are equal to each other, what is the measure of one of those angles?

Which of these quadrilaterals has exactly one pair of parallel sides?

A regular polygon has an exterior angle of $x$ and an interior angle of $5x$. Find the number of sides.

In a circle, any two radii form what kind of shape at the center?

If you double the radius of a circle, what happens to the diameter?

Which part of the circle is used to define its size most commonly in formulas?

The radius of a circle is $10.5$ cm. What is the length of the diameter?

A bicycle wheel has a radius of $30$ cm. If the wheel rolls along the ground for $10$ complete rotations, what is the total distance covered? (Use $\pi \approx 3.14$)

Which of the following is the correct unit for the area of a circle if the radius is measured in centimeters?

Find the circumference of a circle with a diameter of $0.5$ m. (Use $\pi \approx 3.14$)

The area of a sector of a circle of radius $14\text{ cm}$ is $154\text{ cm}^2$. What is the central angle of the sector?

A circular buffer zone of $2\text{ m}$ is created around a circular helipad of diameter $20\text{ m}$. What is the area of the buffer zone? (Use $\pi = 3.14$)

If the area of a circle is $154\text{ cm}^2$ and $\pi = \frac{22}{7}$, what is the length of the longest chord in the circle?

How many faces of a square-based pyramid are triangles?

How many edges meet at each vertex of a cube?

A net with 2 triangles and 3 rectangles forms which 3D shape?

Which 2D shape is the top view (plan) of a cuboid?

When drawing a cube using an oblique projection, which face of the object is typically drawn as a true square without any distortion of its angles or side lengths?

In a one-point perspective drawing, what is the geometric term for the specific point on the horizon where all parallel edges representing depth appear to meet?

A 3D solid is constructed using several $1 \text{ cm}^3$ cubes. Its front elevation shows a single horizontal row of 3 cubes, and its side elevation also shows a single horizontal row of 3 cubes. What is the minimum number of cubes that could be used to build this solid?

A net for a solid has 10 faces. If 2 are octagons and 8 are rectangles, how many edges does the resulting solid have?

If you rotate a 3D drawing of a cylinder $90^{\circ}$ about an axis perpendicular to its length, which view changes from a rectangle to a circle?

A 3D object is formed by a net with 2 pentagons and 5 squares. How many vertices does the object have?

Point $W$ at $(0, -5)$ is reflected across the $x$-axis and then translated $5$ units down. What is the final coordinate?

Point $V$ at $(3, 3)$ is translated $1$ unit up, $1$ unit up, and $1$ unit up. What is the final coordinate?

Point $U$ at $(4, 2)$ is translated $2$ units down and then rotated $90^{\circ}$ clockwise about the origin. What is the final coordinate?

A point at $(1, 1)$ is reflected across the $x$-axis and then reflected across the $y$-axis. What is the final coordinate?

Which combination of transformations does NOT preserve the size of the shape?

A point $(2, -5)$ is reflected across the $y$-axis and then translated $2$ units to the right. What are the final coordinates?

A shape is rotated $90^\circ$ clockwise about the origin and then rotated $180^\circ$ about the origin. This is equivalent to a single rotation of how many degrees counter-clockwise?

Reflecting a point in the $y$-axis and then rotating it $180^{\circ}$ is the same as which single transformation?

A point is translated by $\begin{pmatrix} 1 \\ 2 \end{pmatrix}$, then rotated $180^{\circ}$ about the origin. If the final image is $(-4, -6)$, what was the original point?

Point $H(a, b)$ is reflected across the $x$-axis to $H'$. $H'$ is reflected across the $y$-axis to $H''$. $H''$ is reflected across the $x$-axis to $H'''$. If $H'''$ is $(2, 3)$, what is $a + b$?