📐 geometry

1. **State the problem:** We have a triangle \(\triangle DEF\) with vertices \(D(1,6)\), \(E(2,-5)\), and \(F(-4,-2)\). A dilation centered at the origin with scale factor 2 is app

1. **State the problem:** We need to prove that triangles $\triangle GHJ$ and $\triangle GKJ$ are congruent given that $GH \perp HJ$, $GK \perp KJ$, and $GH = GK$. 2. **Identify th

1. **Problem Statement:** Given triangle points A, B, C, and D with BC \cong DC and \(m\angle ACB > m\angle ACD\), determine the relationship between segments AB and AD. 2. **Key I

1. **State the problem:** We have a right triangle with hypotenuse length 17 cm. The height is 7 cm longer than the base. We need to find the base and height. 2. **Set variables:**

1. **Problem statement:** We have a trapezoid with two diagonals intersecting inside it, forming an angle $x$ at the intersection. Two angles near the intersection are given: $38^\

1. **State the problem:** Stephanie puts 30 cubes in a box. Each cube is $\frac{1}{2}$ inch on each side. The box holds 2 layers with 15 cubes in each layer. We need to find the vo

1. **State the problem:** We need to find the values of $x$ and $y$ in the given circle diagrams and the length of line segment $CE$. 2. **Analyze the first diagram:** The angle at

1. The problem asks which of the given angles could be the size of an exterior angle of a regular polygon. 2. The formula for the exterior angle $E$ of a regular polygon with $n$ s

1. The problem states that \(\angle 1\) and \(\angle 2\) are vertical angles, and their measures are given as \(m\angle 1 = (7x - 9)^\circ\) and \(m\angle 2 = (6x + 11)^\circ\). We

1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal $t$, find the value of $x$ when the angles $(5x - 8)^\circ$ and $(4x + 8)^\circ$ are given a

1. The problem asks to find the distance between the points $A(0,0)$ and $B(-5,-6)$ on the coordinate plane. 2. The distance formula between two points $A(x_1,y_1)$ and $B(x_2,y_2)

1. **State the problem:** We need to find the area of a circle with a diameter of 14 mm. 2. **Formula for the area of a circle:** The area $A$ is given by the formula

1. **Stating the problem:** Identify which letter labels correspond to a major arc, a minor sector, and a major segment based on the given circle diagrams. 2. **Definitions and for

1. **State the problem:** We are given a triangle with vertices A, B, and C, and we need to find the smallest angle to the nearest degree. 2. **Identify the shortest side:** The sm

1. **State the problem:** We need to find the value of the angle $j$ given two adjacent angles $49.5^\circ$ and $79.3^\circ$ that together with $j$ form a straight line. 2. **Recal

1. **Problem statement:** Given a figure where $QR = 15$ and $QS = 45$, find the length of $RS$. 2. **Understanding the problem:** Points $Q$, $R$, and $S$ are on a line or form a

1. **Stating the problem:** We have a cube with side length 10 cm. Point M is the midpoint of segment TS. A string runs from point P to point Q passing through M. We need to find t

1. **Problem statement:** Find the value of $r$ in the first figure where two parallel lines are intersected by a transversal, and the angles given are $50^\circ$, $110^\circ$, and

1. **State the problem:** We are given a kite PLAY with PA = 12 cm and LY = 6 cm. We need to find the area of kite PLAY.

1. **Problem statement:** We have a frustum formed by removing a small cone from a larger similar cone. The small cone has radius $6$ m and height $10$ m. The frustum height is $50

1. **State the problem:** We need to find the volume of the frustum of a rectangular-based pyramid. The frustum is formed by cutting the original pyramid horizontally. 2. **Given d