📐 geometry

1. གྲུ་བཞི་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ཀྱི་འགྲུབ་འབྲས་ག་རེ་ཡིན་ཞིག་བསྐྱར་བཤད་གནང་བ་དགོས། 2. གྲུ་བཞི་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ནི་གྲུ་བཞི་གི་ཁ་ཕྱོགས་དང་པང་གསུམ་གྱི་ཁ་ཕྱོགས་ཡིན། དེ་ནི་གྲུ་བཞ

1. **State the problem:** We are given a rectangular prism with points A, B, C, D on the front face and E, F, G, H on the back face. We know the lengths CD = 2 cm, DE = 3 cm, and B

1. **State the problem:** We have two similar cylinders. The smaller cylinder has a volume of 800 cm^3 and a height of 10 cm. The larger cylinder has a height of 15 cm. We need to

1. **State the problem:** We are given a rectangular prism with points A, B, C, D, E, F, G, H and lengths CD = 65 cm, DE = 63 cm, and BD = 85 cm. We need to find the length of the

1. **State the problem:** We are given a circle with points D, C, A, and B. Point C lies on the vertical segment from D to A inside the circle. We need to find the angle $x^\circ$

1. **Problem statement:** Given a rectangular cuboid with points A, B, C, D on the front face and E, F, G, H on the back face, and given lengths CD = 20 cm, DE = 60 cm, and BD = 40

1. The problem is to plot the point $P(3, 4, -4)$ in a three-dimensional coordinate system. 2. The point $P$ has coordinates $x=3$, $y=4$, and $z=-4$.

1. The problem asks to identify which labelled angles on the triangular prisms are right angles. 2. A right angle measures exactly $90^\circ$.

1. نبدأ بتحديد طول السبلاج شاكي من الشكل المعطى، حيث طول السبلاج هو مجموع الأضلاع التي تحتوي على جذور. 2. الأضلاع المعطاة هي:

1. The problem asks to identify which labelled angles among a, b, e, f, and g on two triangular prisms are right angles. 2. A right angle measures exactly 90 degrees.

1. نبدأ بقراءة المسألة: مساحة قاعدة المبتدع هي 675 دامج مربع، وطول القاعدة ثلاث أضعاف عرضها. 2. نفرض أن عرض القاعدة هو $x$، إذن طول القاعدة هو $3x$.

1. **State the problem:** We need to prove that triangle ACB is isosceles, meaning two of its sides are equal in length. 2. **Identify the points:** Let the coordinates of points A

1. The problem states that $AH = HB$ and $CH$ is perpendicular to $AB$. We need to analyze the geometric properties given these conditions. 2. Since $AH = HB$, point $H$ is the mid

1. **Problem 1:** Given triangle $ABC$ with point $H$ on $AB$ such that $AH \perp AB$ and $CH \perp AB$. We want to understand the properties of $\triangle ACB$ and the point $H$.

1. The problem involves finding the measure of angle $b$ in a triangle where the external angles at $a$ and $c$ are given as $65^\circ$ and $132^\circ$ respectively. 2. Recall that

1. **State the problem:** We have two intersecting diagonal lines crossing a horizontal line, forming angles labeled as follows: the upper left and right angles next to the horizon

1. The problem involves two intersecting lines forming vertical angles with labels 3x, x, x, and y. 2. Vertical angles are equal, so the angle labeled 3x is equal to the angle labe

1. The problem involves a right triangle with angles labeled $130^\circ$, $y$, and $x$, and a right angle of $90^\circ$. We need to find the values of $x$ and $y$. 2. Recall that t

1. **State the problem:** We have two intersecting lines forming vertical angles. The angles around the intersection are labeled as $x$, $x$, $3x$, and $y$. We need to find the rel

1. **State the problem:** We need to find the area of quadrilateral EFGH with given side lengths: EH = 8 cm (vertical), HG = 11 cm (horizontal), GF has a vertical height of 4 cm, a

1. **State the problem:** We need to find the bearing from point F to point G on a square grid map. 2. **Identify coordinates:** Assume each square represents 1 km. Let the coordin