📐 geometry

1. **State the problem:** We are given a rhombus WXYZ with given angles: angle XYZ = 65°,

1. **State the problem:** We need to find the area of the compound figure described. 2. **Analyze the shape:** The shape is a large rectangle with a smaller rectangular notch remov

1. The problem is to find the distance between two points using the distance formula. 2. The distance formula between points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $$d=\sqrt{(x_2-x_1)^2+

1. The problem asks to find the value of $h$ for point $Q(h, 5)$, given points $P(-7, -3)$ and $R(8, 9)$ forming a right triangle with $Q$ on the hypotenuse. 2. Since $Q$ lies on t

1. Stating the problem: We need to find the value of $h$ for the right triangle with vertices $P(-7,-3)$, $Q(h,5)$, and $R(8,9)$, where the right angle is at point $P$. 2. Since th

**Exercice 3 :** 1. Soit ABC un triangle, E est point tel que $\overrightarrow{AE} = \frac{1}{2} \overrightarrow{AB}$, donc E est le milieu du segment [AB].

1. The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves using ordered pairs $(x,y)$. 2. It consists of two perpendicular number lines: t

1. **Énoncé du problème :** On a les mesures orientées suivantes entre vecteurs :

1. **State the problem:** We have trapezium ABCD with AD parallel to BC.

1. **Identify which figure represents an angle.** - (a) → is a ray, not an angle.

1. Le problème demande de déterminer plusieurs mesures principales d'angles orientés entre différents vecteurs donnés. Données :

1. **Problem statement:** We have two circles with centers A and B each of radius 10 cm. B lies on circle A, so AB = 10 cm. Points C and D are intersections of the circles. E is on

1. The problem is about reflecting a triangle across a line (usually the x-axis or y-axis) to obtain its mirror image. 2. To reflect a triangle over the x-axis, take each vertex wi

1. The first problem asks to find the size of all angles in a right triangle where one angle is $90^\circ$ and the other two angles are unknown. 2. Since the triangle is right-angl

1. The problem is to find the missing angles in several triangles, each with a 90° right angle, using properties of angles in a triangle, straight lines, and at a point. 2. We know

1. The problem states that the area of a circle is given as 20 and the diameter is given as 10, which implies the radius $r$ is 5 because $r = \frac{diameter}{2} = \frac{10}{2} = 5

1. Let's clarify the problem: We have a rectangle with one side marked by 1 tick (shorter side) and the other by 2 ticks (longer side). 2. Assuming the shorter side length is $x$ u

1. Let's clarify the problem statement: We are working with a rectangle where the longer side is marked with double 2 tick marks, while the shorter side has a single 2 tick mark. 2

1. **State the problem:** We need to find the reflection of triangle ABC over the vertical line \(\ell\) given by \(x=1\). The vertices of the original triangle are \(A=(3,-4)\), \

1. **Problem Statement:** We need to understand the position of the corner relative to the diameter. It is given that the corner touches the diameter but is not at its midpoint. 2.

1. **State the problem:** We have a semicircle with diameter 10 and a rectangle inscribed inside it. One corner of the rectangle is at the midpoint of the diameter, and the opposit