📐 geometry

1. The problem involves finding the value of the angle labeled \(g\) in a circle with chords intersecting inside and given other angles \(e=31^\circ\) and \(f=40^\circ\).\n\n2. Rec

1. We are given two orange rectangles A and B on a coordinate grid. Rectangle A has corners at approximately (1,1), (3,1), (3,2), and (1,2).

Problem: Find the volume of each figure. Round the answer to two decimal places. Use $\pi=3.14$ for problems 1–5 and use the exact symbol $\pi$ (with an exact expression) for probl

1. **Calculate XY in triangle XYZ** Given: $XZ=6$ cm, $ZY=14$ cm, right angle at $Z$.

1. The problem requires us to complete the table by finding missing diameters and areas of circles given some radius and diameter values. We use the formulas: - Diameter $d = 2r$ w

1. The problem asks us to find the value of $x$ in a triangle where the angles are $x$, $2x$, and $3x$. 2. We know the sum of the angles in any triangle equals $180^\circ$. So we c

1. The problem involves proving congruence relationships between geometric figures, specifically given $\overline{CE} \cong \overline{UW}$ and $\angle C \cong \angle U$. 2. From th

1. **State the problem:** We need to determine the type of triangle congruence based on vertex labels W, V, U. 2. Since the problem describes vertices W, V, U of a triangle but doe

1. The user's question "so what is the triangle" is unclear since it lacks context. 2. A triangle in mathematics is a polygon with three edges and three vertices.

1. The problem is to understand the SSS, SAS, and ASA criteria for triangle congruence. 2. SSS (Side-Side-Side) means if three sides of one triangle are equal to three sides of ano

1. The problem asks to classify the triangle formed by vertices V, U, and W based on its sides or angles. 2. Without numeric coordinates or side lengths, we can only analyze classi

1. Identify the solids and find surface area and volume: 1. Cone: height $h=30$, radius $r=13$.

1. **Identify and calculate surface area and volume of solids:** **(1) Cone:** Given height $h=30$ units and radius $r=13$ units.

1. Find the surface area and volume of a cuboid with length 5, width 3, and height 4. 2. Find the surface area and volume of a cone with radius 3 and height 4.

1. **Find the area of the shaded sector with radius 6 cm and angle 90°.** The formula for the area of a sector is $$\text{Area} = \pi r^{2} \times \frac{\theta}{360}$$ where $r$ is

1. Let's start by understanding what a transformation is: it's like changing a shape or picture on a graph by moving it, flipping it, or making it bigger or smaller. 2. A combining

1. Проблем: Израчунајмо дужину основице $a$ једнакокраког троугла користећи Питагорину теорему. Дати су крак $b=29$ cm и висина $h=21$ cm. 2. Примењујући Питагорину теорему на прав

1. A dilatation is a type of transformation in geometry that changes the size of a shape but keeps its shape the same. 2. Imagine you have a small triangle, and you want to make a

1. Dilatation, also known as dilation, is a transformation in geometry where a figure is enlarged or reduced from a fixed point called the center of dilation. 2. The size changes,

1. प्रश्न दोन आकृतींबाबत आहे: एक वर्तुळ (circle) आणि त्या वर्तुळात एक चौकोन (square) आहे. 2. वर्तुळावर चार संख्या दिलेल्या आहेत: वर 24, उजवीकडे 16, खाली 19, आणि डावीकडे प्रश्नचिन्ह

1. The problem is to understand the side length ratios in a 30°-60°-90° right triangle. 2. A 30°-60°-90° triangle is a special right triangle where the angles are 30 degrees, 60 de