📐 geometry

1. The problem involves checking calculations related to trigonometric functions (sin, cos, tan) and the Pythagorean theorem. 2. The Pythagorean theorem states that in a right tria

1. **Problem Statement:** Draw and label a vector $\overrightarrow{CD}$ intersecting a line segment $\overline{AB}$, with plane P containing $\overline{AB}$ but not $\overrightarro

1. **Problem statement:** Find the height of triangle ABC where sides AB and BC are 10 units each, base AC is 8 units, and a perpendicular from B to AC divides AC into two equal pa

1. **Stating the problem:** Given that the measure of angle $X$ is 75 degrees and the measure of an exterior angle at $Z$ is 160 degrees, we want to find what is true about the val

1. The problem asks to describe the changes in shape, size, position, and orientation of triangle ABC when it is reflected to triangle A'B'C'. 2. Reflection is a transformation tha

1. Problem 8: Find the area of each given figure. Since the figures are described as a right triangle and a right trapezoid, we use the following formulas:

1. **State the problem:** Find the value of $x$ in each of the given figures. 2. **Figure (1):** The triangle has sides 5, 3, and $x$, with a base length 11.

1. **Problem:** Determine which sets of numbers can be the lengths of the sides of an obtuse-angled triangle. 2. **Formula and rule:** For a triangle with sides $a$, $b$, and $c$ w

1. Muammo: Uzunligi 10 m bo‘lgan simyog‘och shamol ta’sirida 27° burchak hosil qilgan holda devorga tushgan. 2. Maqsad: Simyog‘och devorga tegayotgan nuqtasidan uning uchigacha bo‘

1. The problem asks how two triangles are similar. 2. Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

1. **Problem Statement:** We have two vertical parallel walls, one 4 meters high and the other 6 meters high. A man stands upright between them, and we want to find the height of t

1. **Problem statement:** We have points A, B, C, D, and E on a circle, and FG is a tangent to the circle at point C. We know these angles:

1. مسئله: دایره‌ای با شعاع 4 داریم و نقطه‌ای خارج از دایره به فاصله 1 از مرکز دایره است. می‌خواهیم تعداد وترهایی که طولشان 2 است و از این نقطه عبور می‌کنند را پیدا کنیم. 2. فرمول‌ه

1. مسئله: دایره‌ای با شعاع $4$ داریم و نقطه $M$ در فاصله $1$ از مرکز دایره قرار دارد. می‌خواهیم تعداد وترهایی که طولشان $2$ است و از نقطه $M$ می‌گذرند را پیدا کنیم. 2. فرمول وتر: ط

1. We are asked to find the area of a triangle with vertices at points (1, 0), (2, 2), and (3, 1) using the determinant method. 2. The formula for the area of a triangle given vert

1. The problem is to understand the formulas for the perimeter and area of common plane figures. 2. The perimeter of a plane figure is the total length around the figure. It is fou

1. **State the problem:** We have points A, B, C, and D on a straight line with AC = 98 cm and AB = 35 cm. We need to find BC and then find AD given BC is 3 times CD. 2. **Find BC:

1. **Problem Statement:** Given points on a number line and segments labeled with lengths and angles, we want to analyze the geometric relationships and calculate distances involvi

1. مسئله: در محور داده شده، نقطه‌ی A کدام عدد را نشان می‌دهد؟ 2. توضیح: محور اعداد از 0 تا 8 شماره‌گذاری شده است.

1. **Énoncé du problème :** Soit un carré ABCD et un point G défini comme barycentre des points A, B, C, D avec les coefficients respectifs 2, -1, 2, 1.

1. Problem: Find the missing side (square) in a triangle with sides 3 (left), 6 (right), and 12 (bottom). Formula: Use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^