📐 geometry

1. **State the problem:** We need to find the value of angle $c$ in a triangle where one interior angle is $24^\circ$ and the exterior angle adjacent to $c$ is $60^\circ$. 2. **Rec

1. المشكلة: لدينا مثلثان متشابهان أ ب ج ≈ د س ص ع 2. المطلوب: إيجاد طول ب ج و س ع

1. **Problem Statement:** Find the perimeter of the base of a rectangular prism where the base edges are 4 cm and 6 cm. 2. **Formula:** The perimeter $P$ of a rectangle is given by

1. **Problem Statement:** Given points A(9, 8), B(12, 4), and C(4, -2), solve the following:

1. **Problem Statement:** We have a 3 × 4 rectangle made of identical sticks. We want to find how many sticks are needed to construct a 40 × 50 rectangle. 2. **Understanding the pr

1. **Stating the problem:** In triangle $\triangle ABC$, we have $AB = BC$, $\angle ABC = 40^\circ$, and $\angle GAC = 40^\circ$. We need to find the value of $\angle DGC$. 2. **Un

1. **Stating the problem:** Given a triangle with angles \(\angle D = 134^\circ\) (exterior angle), \(\angle A = 62^\circ\), and \(\angle B = 25^\circ\), find the unknown interior

1. **Problem statement:** We have a circular island centered at $P(0,0)$ with radius 8 km. Four pirates want to divide the island into four equal areas by placing their bases so th

1. **Problem Statement:** Given triangle ABC with point D above BC such that AB = BD, BD is perpendicular to AC, and angles at A, D (near B), and C are labeled $x^\circ$, $x^\circ$

1. **Nêu bài toán:** Cho hình vuông ABCD, điểm E, F lần lượt thuộc các cạnh BC và DC sao cho \( \angle CAE = \angle DAF \). Chứng minh rằng EA là phân giác của \( \angle BEF \). 2.

1. Problem: Oblicz obwód trójkąta równoramiennego, jeśli opisany na nim okrąg ma promień $R=13$ cm, a wysokość poprowadzona do podstawy wynosi: a) $h=20$ cm

1. **State the problem:** Find the surface area of a sphere given its radius $r$. 2. **Formula:** The surface area $A$ of a sphere is given by the formula:

1. Stwierdzenie problemu: Obliczamy obwód trójkąta równoramiennego, gdy znany jest promień okręgu opisanego $R=13$ cm oraz wysokość $h$ opuszczona na podstawę. 2. Wzory i zasady:

1. The problem is to understand the classification and properties of parallelograms. 2. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

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 $C(-2;0)$.