📐 geometry

1. **Problem Statement:** We have a square with vertices at $(-1,1)$, $(3,1)$, $(3,-3)$, and $(-1,-3)$, and circles defined by equations such as $(x+1)^2+(y-1)^2=4$, $(x-1)^2+(y+1)

1. **Problem Statement:** We have a square with vertices at $(-1,1)$, $(3,1)$, $(3,-3)$, and $(-1,-3)$ in the $xy$-plane. A circle is tangent to all four sides of this square. We n

1. **State the problem:** Determine the most descriptive name for quadrilateral PQRS using the slope and distance formulas.

1. **State the problem:** Safana has a right rectangular prism with edge lengths $3 \frac{1}{2}$ ft, $2 \frac{1}{4}$ ft, and $4 \frac{1}{3}$ ft. She wants to fill it completely wit

1. **Problem statement:** We have a triangle with interior angles 18°, x°, and an exterior angle of 66° adjacent to the angle x°. We need to find the value of x. 2. **Key concept:*

1. **Problem statement:** We have a triangle with an exterior angle of 66° formed by extending one side. Inside the triangle, one angle is 18° and the angle opposite the exterior a

1. **Problem statement:** We have a triangle with an interior angle $18^\circ$, another interior angle $x^\circ$, and an exterior angle adjacent to $x$ measuring $66^\circ$. We nee

1. **Problem statement:** We have a triangle with an exterior angle of 76° formed by extending one side. Inside the triangle, two angles are given: $x^\circ$ and 51°. We need to fi

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.