Geometry

In the following figure, how many points are marked on the line segment $GH$?

Identify the side opposite to vertex $D$ in the triangle $DEF$.

A circle is drawn with center $C$ and radius $CR$. What is the line segment $CR$?

Which point represents the vertex of the angle $AOB$?

Which of the following describes the relationship between the two circles shown?

In the given diagram, how many rays originate from the point $V$?

Identify the pair of opposite angles in the quadrilateral $ABCD$.

A curve is drawn such that it starts and ends at the same point without crossing itself. If this curve is made of $4$ straight line segments of equal length and all interior angles are $90^\circ$, what is the specific name for the region enclosed?

An angle measures $40^\circ$ more than its supplement. What is the measure of the smaller angle?

A circular garden is surrounded by a path. The radius of the garden is $7$ m and the width of the path is $3$ m. If a straight fence is built from the center of the garden to the outer edge of the path, what is the length of this fence?

A triangle is shown in the figure below. Based on the lengths of its sides, identify the type of triangle if all three sides $AB$, $BC$, and $AC$ are equal to $5\text{ cm}$ each.

A polygon where all sides and all angles are equal is called a:

What type of angle is an angle that measures $120^\circ$?

What do we call a polygon with 4 sides?

What is the sum of all the exterior angles of any convex polygon?

If the three angles of a triangle are in the ratio $1:2:3$, find the measure of the largest angle.

How many diagonals can be drawn from a single vertex of a hexagon?

A piece of wire is bent into the shape of a regular decagon (10-sided polygon). If a student further bends it to form a regular pentagon, how does the interior angle change?

In an equilateral triangle $ABC$, the altitude $AD$ is drawn to the base $BC$. If $\angle BAD = x$, and in a square $PQRS$ the angle between a side and a diagonal is $y$, find the value of $y - x$.

Consider a triangle $XYZ$ where the side $XY = 8\text{ cm}$ and $YZ = 15\text{ cm}$. If the triangle is a right-angled triangle with the right angle at $X$, what is the length of the third side $XZ$?

A solid figure has 6 faces, all of which are congruent squares. Identify the name of this three-dimensional shape shown in the diagram.

Identify the shape that has 12 edges, 8 vertices, and 6 faces, where not all faces are necessarily squares.

How many flat surfaces does a cone have?

What is the minimum number of rectangular faces a cuboid can have?

Which of the following 3D shapes has the same number of vertices as a cuboid?

A cone is cut by a plane parallel to its base. The smaller shape removed from the top is a:

Which 3D shape is represented by a typical unsharpened pencil (ignoring the lead and the eraser)?

A tent is in the shape of a cylinder of radius $5\text{ m}$ and height $3\text{ m}$, surmounted by a cone of the same radius and height $12\text{ m}$. What is the total height of the tent?

Which of the following 3D shapes has the property that every cross-section passing through its center is a circle of the same radius?

A cylindrical roller has a radius of $0.7\text{ m}$ and a length of $2\text{ m}$. When it completes one full rotation, what is the shape of the area it covers on the ground?

In the figure below, a rectangle $PQRS$ is drawn. How many lines of symmetry can be drawn for this rectangle?

An equilateral triangle $ABC$ is shown below. How many lines of symmetry does this triangle have?

A semi-circle has how many lines of symmetry?

The figure shown is reflected across the dotted line. Which side corresponds to side $XY$ in the image?

A kite has how many lines of symmetry?

How many lines of symmetry are there in a regular octagon?

If the word 'MOM' is placed in front of a vertical mirror, how many letters will look changed?

If a shape is reflected across line $L_1$ and then the resulting image is reflected across another line $L_2$ which is parallel to $L_1$, the final position is equivalent to which single transformation?

A circle with center $(0,0)$ is drawn on a coordinate plane. How many lines of symmetry does this figure have?

A rectangle has a length of $8\text{ cm}$ and a width of $5\text{ cm}$. If the rectangle is reflected across a line passing through the midpoints of its lengths, which property of the rectangle changes?

In the given diagram, an arc is drawn from point $P$ intersecting line $L$ at two points $A$ and $B$. To construct a perpendicular to line $L$ from point $P$ using a compass, what is the next step?

Which instrument is used to draw an arc of a given radius?

What is the first step in constructing an angle of $120^\circ$?

To draw a perpendicular to a line from a point lying ON the line, we use the method of ________.

To construct an angle of $15^\circ$, we must first construct $60^\circ$, then ________, and then bisect again.

Which of the following angles CANNOT be constructed using only a ruler and compasses by the method of bisecting standard angles?

In the construction of a $45^\circ$ angle, if we first construct $90^\circ$ and then bisect it, the steps involve using the compasses to draw arcs from which points?

A student needs to construct a line parallel to segment $AB$ passing through an external point $C$. She draws a line through $C$ intersecting $AB$ at $D$. To complete the construction of the parallel line using only a compass and ruler, she must copy which angle at point $C$?

An engineer is constructing a $30^\circ$ angle. He first constructs a $60^\circ$ angle $\angle ABC$ using a compass. To get $30^\circ$, he bisects $\angle ABC$ with ray $BD$. If he then bisects $\angle ABD$, what will be the measure of the resulting smallest angle?

If you are given a circle with a center $O$ and you need to construct a regular hexagon inscribed in it using only a compass, you start by picking any point $A$ on the circumference. What should be the radius of the arcs you draw sequentially around the circle to find the other vertices?