📐 geometry

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:**

1. Problem: Düzgün dördbucaqlı piramidanın yan tili 5 sm, tam səthi 16 sm²-dir. Oturacağının tərəfini tapın. 2. Formullar və qaydalar:

1. **Problem statement:** We need to find the angle between the line segment $AD$ and the horizontal base plane $ABEF$ of the triangular prism. 2. **Understanding the problem:** Th