📐 geometry

1. **Problem statement:** We have a right triangle with a hypotenuse of length 15, an angle of 51°, and the side opposite this angle labeled as $x$. We need to find the length of s

1. **Problem statement:** We need to find the length of the unknown side $x$ in a right triangle where the other two sides are 2 and 5. 2. **Formula used:** According to the Pythag

1. **State the problem:** We need to determine if a triangle with sides $a$, $b$, and $c$ is a right triangle using the Pythagorean theorem. 2. **Recall the Pythagorean theorem:**

1. **Énoncé du problème :** On cherche à démontrer que le point $M(x;y)$ est équidistant des points $S(70;90)$ et $P(90;50)$ si et seulement si $x - 2y + 60 = 0$.

1. The problem is to reflect the point $(-6,-5)$ across the y-axis. 2. When reflecting a point across the y-axis, the $x$-coordinate changes sign (becomes its opposite), and the $y

1. **State the problem:** We have a rectangle divided into small squares, each with an area of $9$ cm$^2$. The rectangle has $5$ squares in height and $6$ squares in width, so ther

1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal $t$, find the value of $x$ given the angles $(6x-1)^\circ$ and $(3x+28)^\circ$. 2. **Identif

1. **State the problem:** We have a compound L-shaped figure with some side lengths given and one unknown vertical side length. We need to find the unknown side length (a) and then

1. **State the problem:** We have a rectangle ABCD with diagonals intersecting. The diagonal segments are given as $5x - 6$ and $3x + 2$. We need to find the value of $x$. 2. **Rec

1. **State the problem:** We have a rectangle with the top side labeled $11x + 2$ and the bottom side labeled $4x + 16$. We need to find the value of $x$. 2. **Recall the property

1. **Problem statement:** We have an isosceles triangle with base 14 m and height $y$ m. Vertical walls $AB$ and $DC$ each have length $x$ m. The segment $BC$ is 8 m. We need to sh

1. **Problem:** What is the relationship between the radius and diameter of a circle? 2. **Formula and Explanation:** The diameter $d$ of a circle is twice the radius $r$. This is

1. **State the problem:** We need to find the volume of a cylindrical pipe excluding the core. The pipe consists of an outer cylinder with radius $12$ cm and height $20$ cm, and an

1. **Stating the problem:** We have a triangle with angles at vertices Z, Y, and X. Given angles are $\angle Z = 47^\circ$ and $\angle Y = 40^\circ$. We need to find $\angle X$ and

1. **Stating the problem:** We are given a diagram with two intersecting lines forming angles labeled 60°, 110°, 51°, and 22°. We need to find the unknown angles \(\angle v\), \(\a

1. **Stating the problem:** We need to find the equation of a circle $k$ centered in the first quadrant. Given:

1. **Problem statement:** We need to find the length of the diagonal $AG$ in a cuboid where $AD = 42$ mm, and the angles at $A$ are $27^\circ$ between $AD$ and $AG$, and $36^\circ$

1. **State the problem:** We are given two parallel lines $m$ and $n$, and two lines $p$ and $q$ such that $q$ is perpendicular to $p$. We know $m \angle 1 = 30^\circ$ and need to

1. **Problem statement:** Given that lines $r$ and $s$ are parallel, and line $u$ is perpendicular to line $t$, with $m \angle 3 = 50^\circ$, find $m \angle 5$. 2. **Key facts and

1. **State the problem:** We have a right isosceles triangle RST with right angle at T, sides RT = ST = 23 units, and base RS = t. We need to find the measures of angles \(\angle R

1. **State the problem:** Identify the method used to solve for the top base length $x$ of a trapezoid given the bottom base and the lengths of the legs. 2. **Explanation:** The me