📐 geometry

1. **State the problem:** We need to find the area of an isosceles triangle DEF where sides DF and DE are each 25 cm, and the base FE is 16 cm. 2. **Formula for the area of a trian

1. **Problem Statement:** Find the area of an equilateral triangle with side length $10$ cm. 2. **Formula:** The area $A$ of an equilateral triangle with side length $s$ is given b

1. **State the problem:** We have two similar right rectangular prisms, X and Y.

1. The problem states that triangle ABC is similar to triangle XYZ, with angles A and B corresponding to X and Y, respectively. 2. Since the triangles are similar, their correspond

1. **Problem Statement:** (a) Given line segments $\overline{AB} = 7.4$ cm and $\overline{CD} = 3.5$ cm, construct a line segment $\overline{PQ}$ such that

1. The problem states that the areas with base AD are 4, 5, and 1. 2. To analyze this, we need to understand how area relates to base and height in geometry.

1. **Problem statement:** We have a triangle ABC with a point D on segment AB such that $|AD|=1$ and $|BD|=2$. The segment CD is perpendicular to AB, dividing the triangle into 7 p

1. **Problem statement:** Given square ABCD with M, N as midpoints of AB and BC respectively, and E as the intersection of CM and DN. We need to prove:

1. The problem is to understand why 110 degrees is not a central angle. 2. A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) intersect th

1. **Problem 21: Find the measures of angles in rectangle ABCD.** A rectangle has four right angles, so each angle measures 90 degrees.

1. **Stating the problem:** We are given a circle with points A, B, C, and D on the circumference. Inside the circle, triangle BAD is formed. The angle at point B is $35^\circ$, th

1. **Problem statement:** From point $A$ outside circle $(O,R)$, two tangents $AB$ and $AC$ are drawn to the circle, with $B$ and $C$ as tangent points.

1. **State the problem:** We need to find the surface area of a cube-shaped box with side length 8 cm. 2. **Formula:** The surface area $S$ of a cube with side length $a$ is given

1. **State the problem:** We are given a sector of a circle with an arc length $s = 4.5$ cm and radius $r = 3$ cm. We need to find the angle $\theta$ (in radians) subtended by the

1. **Énoncé du problème :** Calculer les distances $BA$, $BC$ et le produit scalaire $\overrightarrow{BA} \cdot \overrightarrow{BC}$ pour les points $A(-1,1)$, $B(0,2)$, $C(1,1)$.

1. **Problem Statement:** We have two similar pentagons RSTUV and JFGHI. Given some side lengths, we need to find the length of side $UV$ in pentagon RSTUV. 2. **Given Data:**

1. **State the problem:** We need to find the composition of transformations that maps triangle $\triangle ABC$ with vertices $A(-4,1)$, $B(-3,4)$, and $C(-2,1)$ to triangle $\tria

1. The problem asks to determine whether pairs of triangles are congruent by SSS, SAS, ASA, AAS, HL, or none based on given markings of sides and angles. 2. Important rules for tri

1. مسئله: یک مربع داریم که نصف آن سبز شده و مثلث باقی‌مانده قرمز شده است. می‌خواهیم بدانیم چه کسری از مربع هنوز رنگ نشده است. 2. ابتدا باید جمع کسری‌های رنگ شده را محاسبه کنیم. نصف

1. **Problem statement:** Rotate quadrilateral SORT with vertices S(6,-6), O(-2,-2), R(-2,3), T(5,2) by 270° about the origin. 2. **Formula for rotation:** A rotation of 270° count

1. **State the problem:** Find the volume of a cone with height $h=3$ units and radius $r=2$ units. 2. **Formula for the volume of a cone:**