📐 geometry

1. **State the problem:** We have a blueprint with a scale factor of 1 in : 35 in, and a wall on the blueprint is 3 inches long. We want to know if the actual wall is long enough t

1. **Stating the problem:** We have a parallelogram with angles labeled $y^\circ$, $3y^\circ$, and $3x^\circ$. We want to find the values of $x$ and $y$. 2. **Recall properties of

1. **Problem statement:** In parallelogram ABCD, points E and F lie on diagonal BD such that AE and CF are altitudes in triangles BAD and BCD, respectively. Show that $AF = CE$. 2.

1. **Problem Statement:** Find the value of $x$ in a triangle where a smaller triangle is formed by connecting the midpoints of the sides of a larger triangle. The larger triangle

1. **Problem statement:** We need to find the measure of angle $x$ formed on the circumference by two chords intersecting inside a circle. 2. **Relevant theorem:** The angle formed

1. **Problem Statement:** Given two triangles \(\triangle KLM\) and \(\triangle JMN\) with sides \(KL=6\), \(LM=10\), \(JK=3\), and \(MN=5\), determine if they are similar and stat

1. **State the problem:** We are given two spheres with radii 11 inches and 5 meters, and we need to find their surface areas and volumes.

1. The problem involves understanding the reflection of a quadrilateral across the vertical line $x = -2$. 2. The line of reflection is given by $x = -2$. This means every point on

1. **Problem statement:** We are given four lines with two pairs of parallel lines: $p \parallel t$ and $r \parallel s$. There is an angle labeled $130^\circ$ and another angle lab

1. **State the problem:** Find the volume of a triangular prism with a right triangle base where the base height is 5 cm, base length is 6 cm, and the prism length (depth) is 10 cm

1. **Problem Statement:** Find the volume of the triangular prism with a triangular base area of 15 cm² and a prism length of 5 cm. 2. **Formula for Volume of a Triangular Prism:**

1. **State the problem:** Raymond has a piece of wrapping paper that measures 1 m by 1 m, which is 100 cm by 100 cm, so the total area of the paper is $100 \times 100 = 10000$ cm$^

1. The problem asks which shapes can be set up in a cookie shaper machine and why, and what these shapes have in common. 2. Convex polygons like the pentagon, hexagon, and octagon

1. The problem asks which shapes can be set up in a cookie shaper machine and what these shapes have in common. 2. Convex polygons like the pentagon, hexagon, and octagon can be se

1. The problem asks for the length of the side of a square. 2. To find the side length of a square, we need to know either the area or the perimeter.

1. **Problem statement:** A square piece of paper has four right isosceles triangles removed, one from each corner. The remaining shape is a rectangle ABCD with sides AB = 12 and B

1. **Énoncé du problème :** On a un angle $\angle ABC$ dont la mesure est donnée, et on trace la médiatrice du segment $[AB]$.

1. **Énoncé du problème :** On a un segment $AC$ et sa médiatrice $BD$. La médiatrice coupe $AC$ en son milieu en $B$, donc $B$ est le point milieu de $AC$.

1. The problem states that a polygon with vertices V(-5,7), U(3,5), T(1,-4), and S(-6,-7) is dilated by a factor of $\frac{1}{4}$ centered at the origin. 2. The formula for dilatio

1. **Problem Statement:** Find the values of angles $a$ and $b$ in the circle diagrams numbered 7 and 8.

1. **Problem Statement:** Given a circle with center O, points A, B, C, and D on the circle such that AOD \perp CB, \angle CAB = 60^\circ, AD bisects \angle CAB, and AC = 10 cm. Fi