📐 geometry

1. **Problem Statement:** We want to create an educational infographic illustrating the Pythagorean Theorem, which states that for a right triangle with legs $a$, $b$ and hypotenus

1. **State the problem:** We need to calculate the volume of a right-angled triangular prism with given side lengths. 2. **Identify the dimensions:** The prism has a triangular bas

1. **State the problem:** We need to find the distance between points $M(4, 0)$ and $L(-2, -3)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $A

1. **State the problem:** Find the distance between points $V(5,7)$ and $U(-1,-1)$. 2. **Formula:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$d

1. **State the problem:** We are given a diagram with two vertical parallel lines and two slanted lines crossing them, forming angles labeled $74^\circ$, $x^\circ$, $66^\circ$, $y^

1. **State the problem:** We need to find which point or points remain unchanged (invariant) when reflected over the vertical line $x=1$. 2. **Reflection rule:** When reflecting a

1. **State the problem:** We have two similar octagons with areas $4$ m² and $25$ m². We need to find the scale factor of their side lengths. 2. **Recall the formula:** For similar

1. **State the problem:** We need to find the area of an irregular polygon with given side lengths and a semicircular arc on the left side. 2. **Analyze the figure:** The figure co

1. **State the problem:** We need to find the value of $x$ given that the total angle $\angle ADC$ is $89^\circ$, and it is composed of two smaller angles: $\angle ADB = 52^\circ$

1. **Problem Statement:** Identify which angle pairs from options A, B, C, D, E, and F form linear pairs. 2. **Definition:** A linear pair consists of two adjacent angles whose non

1. **State the problem:** We are given that segment $ab$ is parallel to segment $dc$, and the measures of three angles: angle one is $112^\circ$, angle two is $4x$, and angle three

1. The problem asks to find the side lengths of polygon ABCDE and the angle measures of polygon FGHIJ after certain transformations. 2. First, note that rotating a figure 360 degre

1. **State the problem:** We need to show that the two pentagons are congruent and describe the sequence of transformations that maps the left pentagon (with vertices B, C, D, E, A

1. **State the problem:** We need to find the coordinates of vertex $C'$ after translating point $C$ 2 units left and 9 units down. 2. **Given:** Original coordinates of $C$ are $(

1. **State the problem:** We need to find the new coordinates of the vertices $C$, $D$, and $E$ after translating the triangle 2 units left and 9 units down. 2. **Recall the transl

1. **State the problem:** We are given two complementary angles \(\angle 1\) and \(\angle 2\) with measures \(m\angle 1 = (7x - 13)^\circ\) and \(m\angle 2 = (6x - 1)^\circ\). We n

1. **State the problem:** We are given two supplementary angles \(\angle 1\) and \(\angle 2\) with measures \(m\angle 1 = 5x + 25\) degrees and \(m\angle 2 = 3x - 21\) degrees. We

1. **State the problem:** We have a pole that is 12 feet tall and a string of lights that is 13 feet long. The string is attached at the top of the pole and anchored to the ground.

1. **State the problem:** We need to find the volume of a stepped 3D solid with given dimensions: top front edge $2$ cm, right slanted edge $5$ cm, left vertical edge $2$ cm, left

1. **State the problem:** We want to identify the third step in the process of copying $\angle ABC$. 2. **Recall the steps to copy an angle:**

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. We need to find the value of $x$ given the angles $(8x-2)^\circ$ and $(9x-14)^\circ$