📐 geometry

1. Énonçons le problème : C et D sont deux points du plan tels que la distance entre C et D, notée $CD$, est égale à 7. 2. Rappelons la définition de la distance entre deux points

1. The problem is to identify the correct formula for the distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$. Recall the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y

1. **Problem Statement:** We have a triangle LMN with LM = 12.4 mm, MN = 7.9 mm and angle NLM = 28^6. We want to calculate the area of the triangle given that angle MNL is acute a

1. **State the problem:** We are given a triangle with angle $\theta$ such that $\cos \theta = \frac{1}{8}$.

1. **Stating the problem:** There are two circles with chords and angles labeled. We need to find the hethered angle and analyze the construction needed for part d, given that 0 is

1. **Problem statement:** We have a circle with a chord subtending two angles $a$ and $b$ at points on the circumference and an inscribed triangle. The center of the circle is poin

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