📐 geometry

1. **Problem statement:** We want to determine the shape obtained by cutting a pyramid vertically in half such that each half retains 2 original faces intact, and the cut face is a

1. **Problem Statement:** We want to find the optimal side length $s$ of equilateral triangular panels to cover a tunnel dome with total surface area $A_{total} = 58058\,m^2$.

1. **State the problem:** Given parallelogram ABCD with diagonals AC and BD intersecting at E, prove that $AE \cong CE$ and $BE \cong DE$. 2. **Recall properties of parallelograms:

1. **Problem Statement:** We want to find the optimal side length $s$ of equilateral triangular panels to cover a tunnel dome with total surface area $A_{total} = 58058\,m^2$.

1. Énoncé du problème : On nous donne plusieurs mesures d'angles et on doit déterminer le type de chaque angle. 2. Rappel des définitions importantes :

1. **Problem Statement:** We want to find the optimal side length $s$ of equilateral triangular panels to cover a tunnel dome with total surface area $A_{total}=58058\,m^2$.

1. **State the problem:** We need to find the size of angle $p$ in a triangle where the other two angles are $287^\circ$ and $119^\circ$. 2. **Recall the rule:** The sum of the int

1. **State the problem:** We need to find the size of angle $p$ in a triangle where the other two angles are $287^\circ$ and $119^\circ$. 2. **Recall the triangle angle sum rule:**

1. **State the problem:** We need to find the size of angle $p$ in a triangle where the other two angles are $277^\circ$ and $116^\circ$. 2. **Recall the rule:** The sum of the int

1. **Problem statement:** We need to find the size of angle $x$ given two parallel horizontal lines crossed by two diagonal transversal lines, with one angle marked $45^\circ$ adja

1. **Problem Statement:** We have a field with a baseline $XY = 400$ m and several points with given distances. We need to:

1. **Problem statement:** Calculate the measure of angle $\angle XYZ$ in triangle $XYZ$ with sides $XY=4$ cm, $XZ=6$ cm, and $YZ=3$ cm. 2. **Formula used:** To find an angle in a t

1. **Problem Statement:** We are given two parallel lines cut by a transversal, creating angles labeled $p$ and $m$. We need to identify the angle fact that connects $p$ and $m$. 2

1. **State the problem:** We need to find the sizes of angles $p$ and $r$ given that there are three parallel lines cut by perpendicular transversal lines, and one angle is $126^\c

1. The problem asks to identify the types of angles marked in three diagrams involving two parallel lines and a transversal. 2. Important angle types when a transversal crosses par

1. **State the problem:** We have two connected angular shapes on a horizontal line with angles labeled $2x^\circ$, $3y^\circ$, $100^\circ$, and $4x^\circ$. We need to find the val

1. **Stating the problem:** Find the equation of a circle with center at $(5, -2)$ and radius $4$ cm.

1. **Énoncé du problème :** Déterminer les coordonnées du point $K$ barycentre des points $(A,2)$ et $(B,3)$ avec $A(-1,1)$ et $B(0,2)$.

1. **State the problem:** We have two similar quadrilaterals IJKL and MNOP. Given side lengths IJ = 13, LK = 19 in IJKL, and side NO = 59 in MNOP, we need to find the measure of si

1. **State the problem:** We have two similar quadrilaterals EFGH and IJKL. We know sides EH = 9.2 and EF = 11 in EFGH, and side LK = 43 in IJKL. We need to find the length of side

1. **Problem statement:** We need to solve for the value of $x$ and find the lengths of segments $AD$ and $DB$ in the given triangle with sides labeled as $BD = 2x$, $DA = x + 2$,