📐 geometry

1. **Énoncé du problème :** On donne les points $A(-1,1)$, $B(2,-4)$, et $C(5,-3)$ dans un repère orthonormé.

1. **Énoncé du problème :** On considère les points $A(-1,1)$, $B(2,-4)$ et $C(5,-3)$ dans un repère orthonormé.

1. **Problem Statement:** We have three identical rectangles arranged vertically and horizontally. The bottom-left corner of the bottom rectangle is at $ (1,4) $ and the top-right

1. **State the problem:** We have a parallelogram EDFY with diagonals ED and FY. We need to find the values of $x$ and $y$ given the angle measures: - Angle at vertex F: $(7x - 5)^

1. **State the problem:** We need to find the value of angle $y$ at point $G$ inside the circle, given angles $72^\circ$ and $108^\circ$ at point $F$, and that line $EFG$ is parall

1. The first question asks for the sum of angles \(\angle BAD + \angle BCD\) in a quadrilateral. 2. Given the options: ① 90° ② 270° ③ 180° ④ 360°, the sum of opposite angles in a c

1. **Problem statement:** We have a right triangle KPR with a right angle at K. A segment KL is perpendicular to the hypotenuse PR, dividing it into two segments PL and LR with len

1. **State the problem:** We need to find the volume of a tunnel with a cross section shaped as a major segment of a circle with radius $2.5$ m and height $3$ m, and length $800$ m

1. **State the problem:** Kayden has 50 m of railing but needs enough railing to go all the way around the roof garden, which is an irregular polygon with given side lengths. 2. **

1. **Problem Statement:** We have a half-open cylinder with length 455 cm, top diameter 110 cm, and bottom diameter 91 cm. The length is divided into 4 equal parts, and we want to

1. **Problem Statement:** We have a half-open cylinder with length 455 cm, bottom diameter 91 cm, and top diameter 110 cm. The cylinder is cut into 4 equal pieces along its length.

1. The problem is to find the surface area or volume of an open half-cylinder with a given length of 455 cm. 2. To solve this, we need more information such as the radius of the cy

1. **State the problem:** We have a triangle with angles 115°, 35°, and an unknown angle $x$. We need to find $x$. 2. **Formula used:** The sum of the interior angles of any triang

1. **State the problem:** We are given two intersecting lines forming angles, one angle is 80° and the adjacent angle is $x$. We need to find the value of $x$. 2. **Recall the rule

1. **Problem statement:** Given parallelogram ABCD with $DA=4$, $DC=5$, and angle $\angle ADC=60^\circ$. (a) Prove that $\vec{AB} + \vec{AC} = 2\vec{AC}$.

1. **Problem statement:** We are given three points $P(2, -4)$, $Q(-4, -4)$, and $R(-4, 6)$ that lie on a circle. We need to find the quadrant in which the center of this circle li

1. **Problem Statement:** We have a quadrilateral with sides 10 cm (left vertical), 8 cm (top horizontal), 8 cm (right vertical), 12 cm (bottom horizontal), and a diagonal inside t

1. **Problem Statement:** Define and describe right-angled triangles and equilateral triangles. 2. **Right-angled Triangle:** A right-angled triangle is a triangle in which one of

1. **Stating the problem:** We are asked to find the formula for the distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$.

1. **State the problem:** Given quadrilateral KLMN with KL parallel to NM, LN bisects angle KNM, angle KLN = 54°, and angle MKN = 35°. Find angle KMN. 2. **Understand the propertie

1. **Problem Statement:** We have two triangles with sides $a$, $b$, and $c$. We need to fill in the blanks for the sums of two sides and compare them to the third side.