📐 geometry

1. **State the problem:** We are given a circle with a radius of 4 cm and an arc measuring 70°.

1. **Problem statement:** We need to describe a sequence of rigid motions (translations, rotations, reflections) that maps figure ABCDEFG onto figure JKLMNPQ, given that they are c

1. **Stating the problem:** We have a polygon with points A, B, C, D, E, F, G, H. Given that $AC=26$, $D$ is the midpoint of $AC$, and $AD=BF$. We need to find the perimeter of the

1. **Problem statement:** Given a circle with center C and points A, B, D on the circumference, where $m\angle C = 35^\circ$, find: a) $m\angle LA$

1. **State the problem:** Find the circumference of a circle with diameter 88 mm to 1 decimal place. 2. **Formula:** The circumference $C$ of a circle is given by

1. **State the problem:** We are given a quadrilateral with angles 113°, 98°, 42°, and an unknown angle $x$. We need to find the value of $x$. 2. **Formula used:** The sum of the i

1. **State the problem:** Megan has two boxes with given dimensions. We need to find the volume of each box and determine which box has the greater volume to decide which one she s

1. **Problem statement:** Given a triangle with an exterior angle of 108° and one interior angle of 40°, find:

1. **State the problem:** A rectangle is dilated by a scale factor of $\frac{1}{2}$ to produce a new rectangle. We need to find the relationship between the perimeter of the origin

1. **State the problem:** We need to find the size of the exterior angle $x$ in a quadrilateral where the interior angles given are $90^\circ$, $80^\circ$, $65^\circ$, and one unkn

1. **State the problem:** We need to find the size of the exterior angle $x$ adjacent to the interior angle of $65^\circ$ in a quadrilateral. 2. **Recall the rule for exterior angl

1. **Problem statement:** We have a triangle with base $AB = 8m$ and a segment $DE$ inside the triangle parallel to $AB$ with length $DE = 5m$. The sides from the top vertex to $B$

1. **State the problem:** We have a parallelogram ABCD with sides labeled as follows: AB = 12x, BC = 10y + 10, CD is parallel to AB, and DA = 6x. We need to find the value of $y$.

1. **State the problem:** We need to find the exterior angles $a$, $b$, and $c$ of a triangle where the interior angles adjacent to $c$ and $b$ are $70^\circ$ and $67^\circ$ respec

1. **Problem statement:** Given that lines AB and CD are parallel, explain why angles $a$ and $d$ are equal, angles $b$ and $e$ are equal, and use these facts to prove that the sum

1. **Problem Statement:** We have a rectangle with top-left corner at $(20, 20)$, width $80$ units (x-direction), and height $60$ units (y-direction downward).

1. The problem asks to determine the coordinates of the other corners of a shape, but the original coordinates or shape details are missing. 2. To find other corners, we typically

1. **Problem statement:** We need to draw a rectangle in a Cartesian coordinate system with width 80 units and height 60 units. The top left corner of the rectangle is at coordinat

1. **Problem Statement:** You want to create a graph paper layout of the city streets and attractions based on the given angle and intersection relationships.

1. **Problem Statement:** You are tasked with designing a city layout with four streets: two parallel streets, and two transversal streets with specific angle relationships and att

1. The problem asks to name a chord for circle D. 2. A chord is a line segment with both endpoints on the circle.