📐 geometry

1. **State the problem:** Find the distance between points $M(-9, -6)$ and $N(-9, -10)$ on the coordinate plane. 2. **Formula used:** The distance between two points $(x_1, y_1)$ a

1. **Problem statement:** If the side length of a square is increased four times, find the percent increase in the area of the square. 2. **Formula for area of a square:** The area

1. The problem asks about the solid formed when a parallelogram is revolved completely around a given straight line. 2. When a 2D shape is revolved around a line, the 3D solid form

1. نبدأ بقراءة المسألة: لدينا معادلتان من شرطين لعمود منصفين: $$PQ = 2x = 9$$

1. **بيان المسألة:** نحن ندرس خصائص مثلث له نقاط X, Y, W, Z حيث W تقع على القطعة XZ.

1. **State the problem:** We have a right circular cylinder with radius $r$ and height $h$. A second cylinder has volume 392 times the volume of the first. We want to find possible

1. **State the problem:** We need to determine if triangles $\triangle COT$ and $\triangle NPA$ are congruent, and if so, by which rule. 2. **Given information:**

1. **Problem statement:** We have a right triangle $\triangle ABD$ with right angle at $B$. The hypotenuse $AD$ is 20 cm. Point $C$ lies on segment $BD$ such that $BC=5$ cm and $CD

1. The problem is to find the volume of a cylinder with radius $r=70$ cm and height $h=18$ cm. 2. The formula for the volume of a cylinder is:

1. Задачата е да намерим лицето на триъгълник с върхове в точките $A(1,1)$, $B(-1,2)$ и $C(2,-1)$.\n\n2. Формулата за лице на триъгълник с върхове $(x_1,y_1)$, $(x_2,y_2)$ и $(x_3,

1. **Stating the problem:** We will explain four important theorems related to circles and tangents. 2. **Angle at centre = 2 × angle at circumference:**

1. Let's analyze the properties of each quadrilateral focusing on diagonals, angles, and parallel sides. 2. Square: All sides are equal, all angles are 90°, and diagonals are equal

1. **Stating the problem:** You asked for an explanation of plane geometry, solid geometry, and coordinate geometry including theory, formulas, rules, and theorems. 2. **Plane Geom

1. **Stating the problem:** You asked for an explanation of plane geometry, solid geometry, and coordinate geometry including theory, formulas, rules, and theorems. 2. **Plane Geom

1. Let's clarify the problem: You want to know if two angles are co-interior angles. 2. Co-interior angles are pairs of angles on the same side of a transversal cutting through two

1. The problem asks to identify the types of angles $\angle ABE$ and $\angle CFB$ in the given geometric figure. 2. From the description, $\angle ABE$ is an angle at vertex $B$ for

1. **State the problem:** Calculate the area of a triangle with base 10 cm and height 6 cm. 2. **Formula for the area of a triangle:**

1. نُعطى زاوية القوة ن = $\frac{2\pi}{6} = \frac{\pi}{3}$، ونقطة م(1،1) على خط عمل القوة. 2. ب هي مسقط ج(2،3) على محور س، إذن ب = (2،0).

1. **State the problem:** We need to find the volume of a rectangular prism with dimensions length $10$ cm, width $4$ cm, and height $8$ cm, but it has two quarter-circle cutouts o

1. **Problem statement:** We need to find the length of side AB in a right triangle where angle B is 62°, side AC (opposite angle B) is 12 cm, and the right angle is at A. 2. **Ide

1. **Problem:** Find the image of the point $(4, 0.3)$ after a dilation with scale factor 2. 2. **Formula:** For dilation centered at the origin, the image of a point $(x, y)$ unde