📐 geometry

1. **State the problem:** We have a right triangle with angles 50°, 90°, and 31°, and one side of length 30 mm opposite the 90° angle. We need to find the missing side $x$ opposite

1. **Problem statement:** We have a right triangle with angles 90° and 45°, and the side opposite the 45° angle is 12 cm. We need to find the missing side $x$, which is adjacent to

1. **Stating the problem:** We need to find the measure of angle $m\angle G$ in quadrilateral $EFGH$. 2. **Given information:**

1. **Stating the problem:** We need to find the measure of angle $\angle G$ in quadrilateral $EFGH$ where $\angle F = 150^\circ$, $EF \cong FG$, and $\angle H$ is a right angle ($9

1. **Stating the problem:** We need to find the length of segment $AB$ in a trapezoid where $DC = 11.5$ units, and $MN = 18.7$ units, with $MN$ parallel to both $AB$ and $DC$. 2. *

1. The problem asks to explain axial (line) symmetry in simple words. 2. Axial symmetry is a geometric transformation where a figure is reflected across a line called the axis of s

1. **State the problem:** We need to find the measures of all angles in an isosceles trapezoid where one angle is given as $82^\circ$. 2. **Recall properties of isosceles trapezoid

1. نبدأ ببيان المشكلة: لدينا ثلاث نقاط $a$, $b$, $c$ ونقطة $i$ هي منتصف القطعة $ab$. المطلوب هو التعبير عن الشعاع $\vec{ac}$ بدلالة الشعاع $\vec{mc}$ و$\vec{ma}$ لأي نقطة $m$. 2. ن

1. نبدأ ببيان المسألة: لدينا ثلاث نقاط $a$, $b$, $c$، و $i$ هو منتصف القطعة $ab$. المطلوب هو إثبات أن الشعاع $\vec{ac}$ يساوي مجموع الشعاعين $\vec{mc}$ و $\vec{ma}$. 2. نعرف أن $i$

1. **Problem Statement:** Given a circle with center $O$, a chord $AB$, and a tangent $PT$ touching the circle at $T$. Line $OC$ is perpendicular to chord $AB$ at point $C$. We nee

1. نبدأ بتحديد المشكلة: نريد إيجاد النقطة $M$ بحيث يكون المتجه $\overrightarrow{CM}$ مساوياً للمتجه $\overrightarrow{AB}$. 2. القاعدة المستخدمة: إذا كان $\overrightarrow{CM} = \ove

1. **State the problem:** We have a solid composed of a hemisphere and a cone joined at their bases. The radius $r$ of both the hemisphere and the cone base is 8 cm. The total surf

1. **State the problem:** We have a solid cylinder of height 11 m and radius 4 m. A cone is removed from the top of the cylinder. The cone has the same base radius 4 m and a slant

1. **Problem Statement:** Given a right-angled triangle with one leg (height) 2.7 m and the other leg (base) 70 cm (0.7 m), and a step pattern along the hypotenuse with steps of 6

1. **State the problem:** We have a parallelogram with angles labeled as follows: top-right angle is $3x + 20$ degrees, bottom-left angle is $2y - 5$ degrees, and bottom-right angl

1. The problem is to understand and identify alternate interior angles in a diagram involving two parallel lines cut by a transversal. 2. Alternate interior angles are pairs of ang

1. **Problem Statement:** Count the number of triangles in the given geometric figure. 2. **Understanding the figure:** The figure is a large triangle with vertices at bottom-left

1. **Problem Statement:** Given a circle with center O and diameter AB, OD is parallel to AC, and EF is the tangent at D. Angle $B\hat{C}D = x^\circ$. We need to find angles $B\hat

1. Bạn yêu cầu vẽ hình nhưng không cung cấp chi tiết về hình cần vẽ. 2. Vui lòng cung cấp thêm thông tin về loại hình hoặc phương trình bạn muốn vẽ để tôi có thể giúp bạn chính xác

1. **Nêu bài toán:** Tính chiều dài đoạn dây văng dài nhất của cầu Cần Thơ, biết chiều cao trụ tháp từ mặt nước là $175,30m$, khoảng cách từ mặt nước đến mặt cầu là $30m$, và chiều

1. **Problem statement:** Given a right triangle $ABC$ with right angle at $A$, point $M$ lies on hypotenuse $BC$. Points $D$ and $E$ are the feet of perpendiculars from $M$ to $AB