📐 geometry

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

1. The problem asks to show that the perimeter of the shaded region is $2\pi + \sqrt{32}$.\n\n2. The shaded region consists of a semicircle with radius 4 and a straight line segmen

1. **State the problem:** We have a cylinder with diameter 20 cm and curved surface area (CSA) 200 cm². We need to find its volume in cm³. 2. **Recall formulas:**

1. **State the problem:** We are given a geometric figure with points B, F, C, E, and A such that angles \(\angle BAE\) and \(\angle BCE\) are right angles, and \(AE = FE\). Given

1. **Problem Statement:** Find the midsegment length of trapezoids and solve for $x$ using the midsegment theorem. 2. **Midsegment Theorem:** The midsegment length $m$ of a trapezo

1. The problem asks for the sum of the exterior angles of an octagon. 2. The key formula to remember is: The sum of the exterior angles of any polygon is always $$360^\circ$$, rega

1. **Stating the problem:** We want to understand the relationship between interior and exterior angles of polygons with examples. 2. **Formula and rules:**

1. **Problem Statement:** (a) Complete the table for a cube solid with uniform cross sections.

1. **Problem statement:** We have a right triangle with a 90° angle at vertex A and a 45° angle between side AC and a dashed line inside the triangle. We want to analyze the triang

1. **Problem Statement:** Explain the types of triangles by sides and angles, and important theorems related to triangles. 2. **Types of Triangles by Sides:**