📐 geometry

1. Тодорхойлолт: Хурц өнцөгт гурвалжныг багтаасан тойргийн төвийг $O$, оройгоос буусан өндрийн суурийг $D$ гэж авъя. 2. Тойргийн төв $O$ нь гурвалжны гурван өндрийн огтлолцол буюу

1. The problem involves understanding and solving questions related to chords, lengths, arcs, and segments in circles, which are common topics in geometry. 2. Key formulas and conc

1. مسئله: طول ضلع $AB$ را با استفاده از نامساوی مثلث پیدا کنیم. 2. نامساوی مثلث می‌گوید که برای هر سه نقطه $X, Y, Z$ داریم:

1. **State the problem:** We need to find values of $t$ and $u$ such that the right triangles $\triangle GHI$ and $\triangle RQS$ are congruent by the Hypotenuse-Leg (HL) Theorem.

1. **State the problem:** We need to find the perimeter of the shaded figure on the grid. 2. **Understand the shape:** The figure covers cells from (0,1) to (1,3) vertically, formi

1. **State the problem:** We need to find the perimeter of the shaded rectangle on the grid with vertices at points (2,0), (4,0), (4,1), and (2,1). 2. **Recall the formula for the

1. **State the problem:** We need to find the perimeter of a quadrilateral with side lengths $\frac{1}{2}$ ft, $\frac{4}{9}$ ft, $\frac{4}{9}$ ft, and $\frac{1}{2}$ ft. 2. **Formul

1. **State the problem:** We need to find the perimeter of a parallelogram with sides measuring $1 \frac{1}{4}$ km and $1 \frac{1}{5}$ km. 2. **Recall the formula:** The perimeter

1. **State the problem:** We need to find the perimeter of an equilateral triangle where each side length is $2 \frac{1}{4}$ kilometers. 2. **Recall the formula for the perimeter o

1. **State the problem:** We need to find the perimeter of a triangle with side lengths $1 \frac{1}{3}$ miles, $2 \frac{1}{4}$ miles, and $1 \frac{1}{3}$ miles. 2. **Formula for pe

1. **State the problem:** We need to find the perimeter of a triangle with side lengths $\frac{3}{4}$ m, $\frac{3}{5}$ m, and $\frac{3}{4}$ m. 2. **Formula for perimeter:** The per

1. Let's start by stating the problem: We want to find the area of a shape or region that results in 9800 square meters. 2. The formula for area depends on the shape. For example,

1. The problem states that a figure has a perimeter of 40 units and an area of 100 units squared. We want to find the new perimeter and area after the figure is dilated by a scale

1. The problem is to express the area of a rectangle using its length $L$ and width $W$. 2. The formula for the area $A$ of a rectangle is:

1. **Problem:** A rectangular prism has a volume of 80 cubic inches. 2. **Formula:** Volume of a rectangular prism is given by $$V = l \times w \times h$$ where $l$ is length, $w$

1. **Problem Statement:** Find the sums of angle pairs given by:

1. **Stating the problem:** We are given a transversal line $t$ intersecting two diagonal lines, creating eight angles numbered 1 to 8. We need to identify pairs of angles for thre

1. **State the problem:** We need to find the perimeter of a right-angled triangle with sides 8 cm (vertical), 3 cm (horizontal adjacent to the right angle), and a base segment of

1. **State the problem:** We have a pentagon with vertices A, B, C, D, E and a center of dilation P. The scale factor is $k=3$. We want to find the image distances from P to each v

1. **State the problem:** Find the area of triangle $\triangle BCD$ with vertices $B(-8,-10)$, $C(10,-10)$, and $D(4,-4)$.\n\n2. **Formula for area of a triangle given coordinates:

1. **State the problem:** We need to find the perimeter of square EFGH with vertices E(8, 10), F(-6, 10), G(-6, -4), and H(8, -4). 2. **Recall the perimeter formula for a square:**