📐 geometry

1. **State the problem:** We have polygon ABCD with vertices at approximately A(2,-5), B(3,-5), C(3,-7), D(2,-7) and its transformed polygon A'B'C'D' with vertices at A'(-6,-2), B'

1. **State the problem:** We have a quadrilateral CAPT with point T at coordinates $T(4,4)$. We need to find the coordinates of $T'$ after reflecting the figure over the x-axis. 2.

1. **State the problem:** We have two parallel lines $m \parallel n$ cut by a transversal, creating angles labeled as $(6x - 16)^\circ$ on line $m$, and $(3x + 17)^\circ$ and $(2y

1. **Problem Statement:** We have triangle RNA with vertices R(-5,7), N(-2,3), and A(-7,3). It is rotated 270 degrees clockwise about the origin to form triangle R'N'A'. We need to

1. **Stating the problem:** We have a polygon transformed by the rule $(x,y) \to (x, y - 8)$. We are given that the area of the new polygon is $\frac{1}{8}$ the area of the origina

1. **State the problem:** We have a line segment EF with points E(6, -4) and F(8, 3). We want to find the coordinates of point F' after rotating point F 90° clockwise about the ori

1. **Problem 1: Find the surface area of the right triangular prism.** The prism has a right triangle base with legs 15 ft and 20 ft, and a slant height (hypotenuse) of 25 ft. The

1. **Problem Statement:** Calculate the perimeter of a shape composed of three squares arranged horizontally, each with side length 10 units, and two semicircles of radius 10 units

1. **State the problem:** We need to find the area of ring B in a target made of two rings and one circle, all sharing the same center. Ring B is the blue ring with an outer radius

1. **Stating the problem:** We are given a circle divided into two sectors by a line, with one sector labeled angle $a$ and the other sector labeled $186^\circ$. We need to find th

1. The problem states that a circle is divided into two adjacent sectors by a line, with one sector labeled $a$ and the other labeled $186^\circ$. 2. We know that the total angle a

1. **Problem Statement:** We are given three problems involving distances on the Earth's surface using longitude and latitude.

1. **Problem Statement:** We have a triangle with sides measuring 19 cm, 22 cm, and 23 cm. We need to order the angles \(\angle A, \angle B, \angle C\) from smallest to largest. 2.

1. **Questão 02: Converter a equação polar da circunferência $r=6\cos(\theta)$ para a forma cartesiana.** A fórmula para converter coordenadas polares para cartesianas é:

1. **Stating the problem:** We have a cyclic quadrilateral inscribed in a circle with angles labeled as 50°, z, 96°, x, 40°, and y. We need to find the unknown angles z, x, and y.

1. The problem asks to construct geometric shapes and tilings based on Euclid's equilateral triangle construction. 2. **Constructing a regular hexagon (1.2.1):**

1. The problem states that the angles $A$, $B$, and $C$ satisfy the equation $A + B + C = \pi$. 2. We want to use this fact to express $A + B$ in terms of $C$.

1. **State the problem:** Three regular polygons A, B, and C meet at a point, and their interior angles are in the ratio $a:b:c=3:4:5$. We need to show that polygon C has twice the

1. **State the problem:** Calculate the surface area of a cylinder with radius $r=2$ cm and height $h=4$ cm. 2. **Formula for surface area of a cylinder:**

1. We are asked to find the surface area of three different cylinders. 2. The formula for the surface area $S$ of a cylinder is:

1. **Problem Statement:** Find the missing angle \(\angle C\) in a right triangle using the cosine ratio.