📐 geometry

1. مسئله: محیط ذوزنقه متساوی الساقین ABCD را با داده‌های $BK=4$، $DC=11$ و $AB=5$ بیابید. 2. فرمول محیط ذوزنقه: محیط برابر است با مجموع طول چهار ضلع:

1. **Énoncé du problème** : Soit $M$ un point du cercle circonscrit $\mathscr{C}$ au triangle équilatéral $ABC$ de côté 2, distinct de $\Omega$ et $A$. On pose $M_1 = S(M)$ et $M_2

1. נניח כי במשולש ABC, AB \perp BC, ו- BD הוא הגובה ליתר AC. 2. נתון כי BE הוא תיכון ליתר AC, כלומר E הוא נקודת האמצע של AC.

1. **Problem statement:** Given triangle ABC with points D and E such that BD \perp CE and DC = BE = \frac{1}{2} BC, prove that triangle ABC is equilateral. 2. **Known facts and fo

1. **Problem 1: Find the centre of enlargement and image of Q(1,1)** under enlargement with scale factor $-3$ that maps $P(3,6)$ to $P_1(7,18)$. 2. The formula for enlargement with

1. **Problem Statement:** Given point $A(-1,-5)$ and its reflection image $A'(3,-3)$, find the equation of the mirror line in the form $ax + by + c = 0$. 2. **Reflection Properties

1. **Problem Statement:** Given point $A(-1,-5)$ and its reflection image $A'(3,-3)$, find the equation of the mirror line in the form $ax + by + c = 0$. 2. **Reflection Property:*

1. **State the problem:** Find the area of the polygon formed by the points $(-5,-4)$, $(2,-2)$, and $(1,3)$. Since there are three points, the polygon is a triangle. 2. **Formula

1. The problem states that the part labeled A is a triangle. We need to analyze or solve something related to this triangle. 2. To work with triangles, common formulas include the

1. **State the problem:** We need to find the area of the polygon divided into three sections A, B, and C with given dimensions: total height 7 m, right segment height 2 m, vertica

1. **Problem:** Determine if the given pairs of triangles are similar, write the similarity statement, and name the theorem used. 2. **Key Theorems for Triangle Similarity:**

1. សូមបញ្ជាក់បញ្ហា៖ អ្នកចង់ដឹងពីរបៀបគណនាអំពីសំណុំរូបត្រីកោណ (Group 1)។

1. **Énoncé du problème :** On donne les points $A(-1,1)$, $B(2,-4)$, et $C(5,-3)$ dans un repère orthonormé.

1. **Énoncé du problème :** On considère les points $A(-1,1)$, $B(2,-4)$ et $C(5,-3)$ dans un repère orthonormé.

1. **Problem Statement:** We have three identical rectangles arranged vertically and horizontally. The bottom-left corner of the bottom rectangle is at $ (1,4) $ and the top-right

1. **State the problem:** We have a parallelogram EDFY with diagonals ED and FY. We need to find the values of $x$ and $y$ given the angle measures: - Angle at vertex F: $(7x - 5)^

1. **State the problem:** We need to find the value of angle $y$ at point $G$ inside the circle, given angles $72^\circ$ and $108^\circ$ at point $F$, and that line $EFG$ is parall

1. The first question asks for the sum of angles \(\angle BAD + \angle BCD\) in a quadrilateral. 2. Given the options: ① 90° ② 270° ③ 180° ④ 360°, the sum of opposite angles in a c

1. **Problem statement:** We have a right triangle KPR with a right angle at K. A segment KL is perpendicular to the hypotenuse PR, dividing it into two segments PL and LR with len

1. **State the problem:** We need to find the volume of a tunnel with a cross section shaped as a major segment of a circle with radius $2.5$ m and height $3$ m, and length $800$ m

1. **State the problem:** Kayden has 50 m of railing but needs enough railing to go all the way around the roof garden, which is an irregular polygon with given side lengths. 2. **