📐 geometry

1. **Énoncé du problème :** Soit un triangle ABC dans le plan avec les points barycentriques définis par les poids donnés. On doit construire et démontrer plusieurs propriétés des

1. The problem is to analyze the properties of a parallelogram by measuring its sides, angles, and diagonals. 2. A parallelogram is a quadrilateral with opposite sides parallel and

1. **State the problem:** We are given a quadrilateral ABCD with sides labeled as follows: CB = $2y - 4$, CD = $4x$, BA = $x + 9$, and DA = $y$. We need to find the values of $x$ a

1. **Problem statement:** We have a rectangle $ABCD$ with diagonal $\overline{AC} = 25$ cm. Point $O$ is the intersection of the diagonals $\overline{AC}$ and $\overline{BD}$. We n

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 2 cm and 4 cm, and a height of 6 cm. 2. **Formula for the area of a trapezoid:**

1. **Problem Statement:** We need to find the area in square meters of an irregular polygon with 12 sides, given the lengths of each side. 2. **Approach:** Since the polygon is irr

1. Problem: Convert 4 m² to dm². 2. Formula: To convert square meters to square decimeters, use the conversion factor $1\text{ m} = 10\text{ dm}$, so $1\text{ m}^2 = 10^2 = 100\tex

1. **Problem Statement:** Given rhombus ABCD with AE = 3x - 5 and CE = x + 3, find $x$, $AE$, $CE$, and $AC$. 2. **Formula and Properties:** In a rhombus, the diagonals bisect each

1. **Problem statement:** We have a pyramid with apex $P$ and rectangular base $ABCD$ where $PA=PB=PC=PD$. The base edges are $DC=13$, $CB=27$, and $AB=16$ cm. We need to find the

1. **Problem statement:** We have a pyramid with apex $P$ and rectangular base $ABCD$. The edges $PA = PB = PC = PD$ are equal. The base sides are $DC = 13$, $CB = 27$, and $AB = 1

1. **المشكلة:** أوجد محيط المثلث (أ ب ج) حيث نصف أقطار الدوائر أ=3، ب=2، ج=1. 2. **المعطيات:** نصف قطر الدائرة أ = 3، نصف قطر الدائرة ب = 2، نصف قطر الدائرة ج = 1.

1. **Problem Statement:** We have a cyclic quadrilateral inscribed in a circle with two pairs of equal sides. One interior angle at the bottom right corner is $38^\circ$, and an ex

1. **Problem 1: Find the slant height $s$ of the square-based pyramid.** Given:

1. **Problem Statement:** Prove that in a circle with center O and diameter AB, the angle at the circumference subtended by AB is a right angle, i.e., $\angle ARB = 90^\circ$. 2. *

1. **State the problem:** We need to solve for side $c$ in a triangle using the Law of Cosines. 2. **Law of Cosines formula:**

1. **Problem statement:** We have a circle with center $O$. Segments $UX$ and $UV$ are tangents to the circle, and $XV$ passes through the center $O$. Given $UV=12.6$ and $XV=12$,

1. The problem is to find the length of the hypotenuse or a missing side in a right triangle using the Pythagorean theorem. 2. The Pythagorean theorem states that in a right triang

1. **Problem Statement:** We have a circle centered at $O$ with tangent segments $\overline{EH}$ and $\overline{EF}$ from point $E$ to the circle. The segment $\overline{HF}$ passe

1. The problem is to create a practice test based on Alberta Grade Nine Circle Geometry. 2. Circle geometry involves properties and theorems related to circles, such as angles, cho

1. **Problem statement:** Determine the values of $d^\circ$, $e$, and $f$ for the given circles with center $O$. 2. **Key circle property:** The angle subtended at the center of a

1. **Stating the problem:** We are given angles \(\angle BAD = (2a + 25)^\circ\) and \(\angle BCD = (3a - 15)^\circ\). We need to find: a. The value of \(a\)