📐 geometry

1. **State the problem:** We need to find the perimeter of a parallelogram given its side lengths. 2. **Identify the sides:** The parallelogram has two pairs of equal sides. One si

1. **State the problem:** We need to find the perimeter of a parallelogram given its vertices on a grid. 2. **Formula for perimeter of a parallelogram:** The perimeter $P$ is given

1. **Problem statement:** We have a solid cube with side length 10 cm. A pyramid-shaped hole is drilled inside it. The pyramid has a square base of side 5 cm and height 5 cm. We ne

1. **Stating the problem:** We have a right triangle with hypotenuse $d = 5.7$ meters and vertical leg $h = 3$ centimeters. We want to find the length of the horizontal leg. 2. **C

1. **Problem:** In the circle with center O, AOB is a straight line. Find the unknown angle \(\angle ACB\). 2. **Formula and rules:**

1. **Problem statement:** Given a circle with points A, B, C, and D on the circumference, where CD is a diameter, AB is parallel to CD, \(\angle BDC = 70^\circ\), and \(\angle BAC

1. مسئله: شما درخواست یک فرمول ساده و قابل فهم دارید. 2. فرمول پیشنهادی: فرمول مساحت مستطیل که بسیار ساده و کاربردی است:

1. **Problem statement:** We have a heptagon (7-sided polygon) with six interior angles each measuring $x^\circ$ and one interior angle measuring $y^\circ$. Given $y = 126$, find t

1. The problem involves finding the values of angles $a$ and $b$ in a circle with points $P, Q, R, T$ on the circumference and given angle measures. 2. Given $m\angle PQT = 180^\ci

1. **State the problem:** We have two congruent trapezoids ABCD and JKLM. Given angles and side lengths in ABCD, find the measure of angle $\angle L$ and the length $JK$ in trapezo

1. **State the problem:** We have two congruent trapezoids ABCD and JKLM. Given some side lengths and angles in ABCD, we need to find the measure of angle $\angle L$ and the length

1. נניח שהבעיה היא למצוא את הערכים של הקטעים EF ו-MN. 2. לפי הנתונים, EF שווה 18 ו-MN שווה 14.

1. **הבעיה:** נתון טרפז ABCD עם בסיסים AB ו-DC, וקטעים EF ו-MN מקבילים לבסיסים. נתונים: $AB=BC=12$ ס"מ, $DC=24$ ס"מ, $AD=18$ ס"מ, $AM=3$ ס"מ, $CF=6$ ס"מ. יש לחשב את אורכי הקטעים EF

1. **Stating the problem:** We will cover the key concepts of the Circle topic for class 10, including definitions, formulas, and example questions similar to previous year board e

1. **Stating the problem:** Quadrilateral ABCD is similar to quadrilateral PQRS. We need to find: (a) The ratio of the length of AB to the length of PQ in the form $1:n$.

1. نبدأ بحل السؤال الأول: إذا كانت الأطوال مقدرة بالسنتيمتر، المطلوب حساب $س + ص$ في الشكل المعطى. 2. بالنظر إلى الشكل، نلاحظ أن هناك علاقات بين الأطوال المعطاة:

1. **Problem Statement:** In the given figure, if $PU = ST$ and $PQ = RS$, prove that $\angle PQU = \angle TRS$. 2. **Given:**

1. **Problem statement:** Given points P(2,9), T(10,-3), R(n,-13), and M as the midpoint of PT in parallelogram PARM, find: 3.1.1 Length of PT

1. **Problem statement:** We are given a triangle with vertices A, B, C, and D, where angle B is 128° and line CD forms approximately an 80° angle with the horizontal line AD. We n

1. **Problem Statement:** Given a cyclic quadrilateral ABCD inscribed in a circle, with triangle ABD isosceles where AD = BD, and angle ABC = 110°. 2. **Goal:** Find the values of

1. **Problem Statement:** We are given a triangle BCD with angle B measuring 128° and points B, C, D positioned on a semicircular protractor. We need to find the size of angle BCD