📐 geometry

1. **State the problem:** We need to find the image of triangle \(\triangle STU\) after reflecting it over the x-axis. The original points are \(S(-4,-3)\), \(T(6,-3)\), and \(U(-4

1. **State the problem:** We are given a triangle with sides |CF| = 22 cm, |EF| = 11.8 cm, and the angle \(\angle EFC = 110^\circ\). We need to find the distance |CE| using the cos

1. **State the problem:** We are given a triangle with sides |CF| = 22 cm, |EF| = 11.8 cm, and the included angle \(\angle EFC = 110^\circ\). We need to find the length |CE| using

1. **State the problem:** We are given a triangle ABC with sides |AB| = 12 cm, |AC| = 10 cm, and angle \(\angle ABC = 37^\circ\). We need to find the size of angle \(\theta = \angl

1. **State the problem:** We need to find the length of the pipe running diagonally from the floor drain at point $(2, 2)$ to the sewer connection at point $(10, 17)$ in a coordina

1. **Problemstellung:** In der Zeichnung sind die Geraden g und h parallel. Gegeben sind die Längen 7,7, 3, 3,5 und 4,4. Gesucht sind die fehlenden Längen $x$ und $y$. 2. **Formel:

1. **State the problem:** Find the volume of the composite solid, which is a stepped rectangular prism with given dimensions 5 cm (height of the step) and 15 cm (depth). 2. **Under

1. **State the problem:** We need to find the volume of a composite solid shaped like an L-shaped stepped rectangular prism by breaking it into rectangular prisms. 2. **Identify di

1. **Stating the problem:** We need to find the angle $j$ in the given polygon with multiple interior and exterior angles. 2. **Understanding the problem:** The polygon has several

1. **State the problem:** We have two tangent segments from an external point A to a circle, touching the circle at points B and D. The lengths of these tangent segments are given

1. **State the problem:** We have a circle with center C and two tangent points B and D. Tangent segments from points B and D to point A are given as expressions in terms of $x$: -

1. **State the problem:** We have a quadrilateral with sides 12 cm (bottom), 5 cm (right vertical), 15 cm (slanted right upper side), and two unknown lengths $x$ (diagonal from bot

1. **State the problem:** We need to find the circumference of a circle with radius $11$ m. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find the circumference of a circle with a diameter of 14 ft. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **Problem Statement:** We have a quadrilateral QRST with given coordinates before and after a reflection. We need to describe the transformation, identify the algebraic rule, fi

1. **Problem:** Reflect triangle JKL over the x-axis and find the coordinates of the image J'K'L'. 2. **Formula for reflection over the x-axis:**

1. **State the problem:** Calculate the area of the L-shaped figure with given side lengths in yards. 2. **Convert mixed numbers to improper fractions:**

1. **Problem statement:** Given that the side of the house and the side of the shed are parallel, find the measures of angles \(\angle 1\) and \(\angle 2\) when one angle is given

1. **Problem Statement:** Given two parallel lines $l_1$ and $l_2$ cut by a transversal, find the measures of the indicated angles $\angle 3$ and $\angle 5$ given that $\angle 1 =

1. **Problem Statement:** We have two similar quadrilaterals. The top-left quadrilateral has angles 90°, 106°, 90°, and 74°. The bottom-center quadrilateral is similar but has one

1. **State the problem:** We have two similar shapes. The left shape has sides 2 mm and $q$ mm, and the right shape has corresponding sides 1 mm and 4 mm. We need to find the missi