📐 geometry

1. **Постановка задачи:** В ромбе сторона равна $12$, тупой угол равен $120^\circ$. Нужно найти меньшую диагональ ромба. 2. **Формулы и правила:** В ромбе все стороны равны, диагон

1. The problem is to draw a triangle. 2. A triangle is a three-sided polygon.

1. **Problem:** Describe a triangle. 2. A triangle is a basic shape in geometry with **3 sides**, **3 angles**, and **3 vertices**.

1. The problem is to draw a rectangle. 2. A rectangle is a quadrilateral with four right angles and opposite sides equal in length.

1. **Problem Statement:** We analyze the first problem (top-left circle) with center $O$, diameter $AB$, and point $C$ on the circle. Given angle $\angle BAC = 47^\circ$, find angl

1. **State the problem:** Given two intersecting lines with angles labeled 1, 2, 3, and 4 around the intersection, and $m\angle 1 = 135^\circ$, find the measures of angles 2, 3, an

1. **Problem Statement:** We have a rectangle with diagonals drawn, intersecting at the center. We are given that one of the angles formed at the intersection of the diagonals on t

1. **State the problem:** We have a triangle with interior angles $35^\circ$, $(5x + 7)^\circ$, and $(9x - 2)^\circ$. We need to find $x$ and the measure of the angle $(5x + 7)^\ci

1. **State the problem:** Find the distance between the points $(9, 5)$ and $(-2, 3)$.\n\n2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given

1. **State the problem:** We have a circle with center P and diameters AC and BE. The circle is divided into arcs with measures given as expressions in terms of $w$: $(4w + 8)^\cir

1. **State the problem:** We are given a rectangular prism with a square front face of side length 6 cm. 2. **Identify the dimensions:** The front face is a square with sides 6 cm

1. **State the problem:** We need to find the volume of a rectangular prism with dimensions 6 cm, 6 cm, and 6 cm. 2. **Formula:** The volume $V$ of a rectangular prism is given by

1. **State the problem:** We need to find the volume of a rectangular prism with dimensions approximately 8 units wide, 10 units tall, and 7 units deep. 2. **Formula for volume of

1. **State the problem:** We need to find the volume of a rectangular prism with dimensions given by the number of unit cubes along its width, height, and depth. 2. **Identify the

1. **State the problem:** Find the volume of a rectangular prism with dimensions 5 units wide, 3 units tall, and 8 units long. 2. **Formula:** The volume $V$ of a rectangular prism

1. **State the problem:** Find the volume of a rectangular prism with dimensions given by the number of unit cubes along its length, width, and height. 2. **Formula:** The volume $

1. **State the problem:** Find the volume of a rectangular prism with dimensions 6 units wide, 8 units tall, and 4 units deep. 2. **Formula:** The volume $V$ of a rectangular prism

1. **State the problem:** We need to find the length of the third side (hypotenuse) of right triangles given the lengths of the two legs. 2. **Formula used:** For a right triangle

1. **State the problem:** Find the measure of angle $\angle KNM$ formed by a tangent and a secant intersecting outside the circle at point $K$. Given that $m\angle KNM = 151^\circ$

1. The problem asks which 3-dimensional figure has a triangular face. 2. Let's analyze each option:

1. **State the problem:** We need to find the volume of a box (rectangular prism) with given dimensions: height = 13 cm, width = 6 cm, and length = twice the width. 2. **Formula fo