📐 geometry

1. **State the problem:** We have a pentagon JKLMN with vertices J(-2,-1), K(2,-1), L(3,-3), M(0,-5), and N(-3,-3). We need to find the coordinates of J' after a 90° clockwise rota

1. **Déterminer la mesure de l’angle θ dans les triangles donnés**. **a)** Dans le triangle RTU, on sait que RT est perpendiculaire à SU, donc l'angle en R est un angle droit de 90

1. **Problem:** Find the coordinates of $S'$ when Figure STUV is rotated 180° about the origin. 2. **Formula for 180° rotation:** Rotating a point $(x,y)$ by 180° about the origin

1. **State the problem:** We have a right triangle with one angle of 45°, the right angle at the top vertex, and the sides labeled as follows: the left slanted side is $x$, the rig

1. **Stating the problem:** Calculate the perimeter $O$ and area $o$ of the rectangle with vertices $A(2,1)$, $B(-2,1)$, $C(-2,-1)$, and $D(2,-1)$.

1. **State the problem:** We are given the volume of a cube as 125 cubic units and need to find the edge length. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is gi

1. **State the problem:** We are given the volume of a cube as 5832 cubic units and need to find the edge length. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is g

1. **Stating the problem:** We have an isosceles triangle with vertices Zero (top vertex), Alawi (bottom-left), and Perin (bottom-right). The angle at Zero between the routes to Al

1. The problem involves understanding an enlargement transformation in geometry. 2. Enlargement is a type of transformation that changes the size of a shape but keeps its shape and

1. **Stating the problem:** We need to construct the images of the line segment [AB] under enlargements with center P and scale factors 2, 3, 3/2, and 1/2.

1. Problema 9: Determinar as coordenadas dos vértices do retângulo [ABCD] sabendo B(6, 2), P(7/2, 1/2) e M(4, 2), onde P é o ponto de interseção das diagonais e M é o ponto médio d

1. The problem asks for the number of line segments on a Tic-Tac-Toe board. 2. A Tic-Tac-Toe board is a 3x3 grid formed by 4 vertical and 4 horizontal lines intersecting.

1. **State the problem:** Find the perimeter of triangle $\triangle ABC$ with vertices $A(-6,4)$, $B(8,-1)$, and $C(0,-9)$. The perimeter is the sum of the lengths of sides $AB$, $

1. **State the problem:** We need to find the circumference of circle O, given the center O at (-3, 2) and a point P on the circle at (-9, -1). 2. **Formula for circumference:** Th

1. **Problem Statement:** (a) Given a circle with arcs $\overset{\frown}{AB} = 170^\circ$ and $\overset{\frown}{AC} = 66^\circ$, find the measure of angle $\angle ADC$ formed by a

1. **Problem Statement:** (a) Given $m\angle AEB = 47^\circ$ and $m\overset{\frown}{AB} = 133^\circ$, find $m\overset{\frown}{CD}$.

1. **Problem Statement:** Determine how many triangles are formed inside a large triangle by a vertical line from the apex to the base, two diagonals, and one horizontal segment in

1. **Problem statement:** We need to find the total number of triangles in a complex figure composed of one large outer triangle with several internal lines creating multiple small

1. **Problem statement:** Determine the area of the shaded triangle AEC in the given figure. 2. **Given information:**

1. **Problem Statement:** You are given rectangle ADCB with area 108 cm², side BA = 6 cm, and DC = ED. You need to find:

1. **State the problem:** We are given a circle with center O and points A, B, C, D on the circumference. We know that \(\angle BCD = 128^\circ\) and need to find \(\angle OBD\).\n