📐 geometry

1. **Problem Statement:** In triangle $\triangle ABC$, $BM$ and $CN$ are perpendiculars from vertices $B$ and $C$ respectively onto any line passing through $A$. $L$ is the midpoin

1. **Stating the problem:** We have a large rectangle divided into 9 smaller rectangles. The perimeters of rectangles A, B, and C are given as 10 cm, 20 cm, and 30 cm respectively.

1. ננסח את הבעיה: נתונה קובייה עם צלעות $AB = u$, $BC = v$, ו-$CC' = w$. נקודות $E$, $F$, ו-$G$ מוגדרות כפי שבסעיף א'. בסעיף ב' נדרש לחשב את הערך של $\lambda$ כך ש-$\angle EFG = 45

1. **State the problem:** Prove that the opposite angles of parallelogram ABCD are congruent, specifically that $\angle B \cong \angle D$.\n\n2. **Given:** $AB \parallel CD$ and $A

1. **Problem Statement:** We have a large square with side length 1 dissected into 14 smaller squares. We need to find the area of the shaded smaller square. 2. **Key Idea:** The t

1. **Problem Statement:** Calculate the perimeter of pentagon ABCDE formed by two overlapping rectangles with given side lengths.

1. **Énoncé du problème :** Déterminer une mesure de l'angle orienté $\left(\overrightarrow{AB};\overrightarrow{AC}\right)$ avec les points $A(-2;2)$, $B(-4;1)$ et $C(-2;0)$.

1. **Problem 1A:** Construct a triangle PQR with sides $PQ=7$ cm, $QR=5$ cm, and angle $\angle PQR=120^\circ$. Then construct another triangle SQR with the same area as triangle PQ

1. **Problem Statement:** Given a line segment NT with length 12 cm, and NT = 12MT, find the radius of the semicircle drawn above NT. 2. **Understanding the problem:** The points M

1. The problem involves understanding the placement of numbers on a plus-shaped graph with intersecting vertical and horizontal lines. 2. The horizontal line has numbers 7 on the l

1. **Problem Statement:** Draw two concentric circles and a chord to the outer circle that is also tangent to the inner circle. 2. **Understanding the Problem:**

1. **State the problem:** We have a square ABCD with side length 10 cm. Two arcs are drawn inside the square: one connecting points A and B, and another connecting points C and D.

1. مسئله را بیان می‌کنیم: آیا عبارت $a+b=c$ در مثلث قائم‌الزاویه‌ای که ضلع‌های آن $a$، $b$ و وتر $c$ است، برقرار است؟ 2. فرمول مورد استفاده: در مثلث قائم‌الزاویه، قضیه فیثاغورس برق

1. Bài toán: Từ điểm $M$ ngoài đường tròn $(O;R)$ vẽ hai tiếp tuyến $MA$, $MB$ với $(O)$. $AC$ là đường kính của $(O)$, $MC$ cắt $(O)$ tại $D$. Trên tia đối $MA$ lấy điểm $N$ sao c

1. Bài toán yêu cầu chứng minh đẳng thức $CM \cdot 4OH \cdot OM = CB \cdot CN$ với các điểm và đoạn thẳng được xác định như sau: - $M$ là điểm ngoài đường tròn $(O;R)$.

1. Diketahui kubus ABCD.EFGH dengan rusuk 8 cm. Hitung cosinus antara garis GC dan bidang BDG. 2. Rumus yang digunakan adalah cosinus sudut antara garis dan bidang, yaitu:

1. The problem is to construct a rectangle ABCD. 2. A rectangle is a quadrilateral with four right angles and opposite sides equal in length.

1. **Problem:** The ratio between two corresponding sides in two similar triangles is 4 : 3 and the perimeter of the smaller triangle is 36 cm. Find the perimeter of the greater tr

1. **Problem statement:** A cone of the highest possible volume is hollowed out from a wooden cylinder. We need to find the ratio of the volume of the remaining wood to the volume

1. The problem asks: How many lines of symmetry does the given zigzag figure have? 2. A line of symmetry divides a figure into two mirror-image halves.

1. مسئله: کاغذ دایره‌ای شکل را تا می‌کنیم و سپس سوراخ یا برش می‌دهیم. پس از باز کردن کاغذ، شکل حاصل را باید تعیین کنیم. 2. برای تحلیل این مسئله، باید بدانیم که هر بار تا کردن کاغذ،