📐 geometry

1. **Problem statement:** When the given net is folded into a cuboid, determine which two points join with point X. 2. **Understanding the net:** The net consists of six rectangles

1. The problem is to find the surface area of a triangular prism given its net on a 1 cm² grid. 2. The net consists of two triangles and three rectangles. The surface area of the p

1. **State the problem:** Rotate the polygon with vertices A(0, -3), B(-6, 0), C(-7, -10), and D(-3, -9) by 270° clockwise around the origin. 2. **Formula for rotation:** Rotating

1. **State the problem:** We need to rotate the shape with vertices A(1,3), B(8,0), C(9,8), and D(2,7) by 90° clockwise around the origin on the coordinate plane. 2. **Formula for

1. The problem is to rotate a shape 90 degrees clockwise around the origin in the coordinate plane. 2. The formula for rotating a point $(x,y)$ 90 degrees clockwise is:

1. **State the problem:** We have a polygon with vertices at points A(-3, 5), B(-7, 2), C(-8, 8), and D(-4, 10). We need to rotate this shape 90° clockwise around the origin. 2. **

1. **State the problem:** We have a shape with points A(-4,0), B(-7,-2), and C(-9,-9). We need to rotate this shape 180° counterclockwise about the origin. 2. **Formula for rotatio

1. **State the problem:** We have two vertical poles, one 16 ft high and the other 24 ft high, standing 30 ft apart. A worker wants to place a stake on the ground between them and

1. The problem asks to find the new coordinates of triangles after applying given translations. 2. Translation means moving every point of a shape by the same amount in a given dir

1. **State the problem:** We are given a diagram with angles expressed in terms of $x$ and $y$ in degrees. We need to find the values of $x$ and $y$. 2. **Identify the angles and r

1. **הבעיה:** נתון כי הנקודה C היא אמצע הקטע AD, ושהקטעים DE ו-AB מקבילים ($DE \parallel AB$). יש להוכיח כי C היא גם אמצע הקטע EB. 2. **הגדרות וכללים חשובים:**

1. **State the problem:** We have triangle ABC with points M on AB and K on AC. Given ratios: $\frac{AM}{MB} = \frac{3}{2}$ and $\frac{AK}{KC} = \frac{2}{3}$.

1. **Stating the problem:** We have triangle ABC with points M on BC such that $BM:MC=2:3$, and point K on segment AM such that $AK:KM=2:1$. We want to find the ratios of areas $\f

1. **State the problem:** We have triangle ABC with a right angle at C, angle A = 120°, side AC = 8, and side BC = 5. We need to find the area $S_{ABC}$. 2. **Recall the formula fo

1. **Problem Statement:** Find the missing interior angle of the Hospital land area, which is a triangle with given angles 63.4° and 45°. 2. **Formula Used:** The sum of interior a

1. **Problem Statement:** We are given an isosceles triangle $\triangle ABC$ with $AB = BC$ and an equilateral triangle $\triangle DEF$ inscribed inside it such that points $D$ and

1. **Problem Statement:** In triangle $\triangle ABC$ with $AB = AC$, points $D, E, F$ lie on sides $AB, BC, CA$ respectively such that $DE = EF = FD$, forming an equilateral trian

1. **State the problem:** We are given a circle with radius $r = 3$ meters and an angle $\theta = \frac{5\pi}{12}$ radians. We need to find the arc length corresponding to this ang

1. The problem asks to draw the plan view of a 3D shape given its front elevation and side elevation. 2. The front elevation shows a red right triangle on a square grid.

1. **Problem statement:** Given circle (O) and point A outside (O), with tangents AB and AC to (O) at points B and C respectively. A secant ADE is drawn such that ray AD lies betwe

1. **State the problem:** We have a triangle ABC with angles $a$, $b$, and $c$. Given: - $a$ is 13 less than $c$, so $a = c - 13$