📐 geometry

1. **Problem statement:** We have a square ABCF and a parallelogram CDEF on the Cartesian plane. Given points F(10,12), D(26,10), and E(18,0), we need to find the coordinates of po

1. **Stating the problem:** We are given points F(10,12), D(26,10), and E(18,0) as part of a polygonal chain with points A, B, C, D, E, and F connected in a specific sequence formi

1. **Problem Statement:** We are given a right-angled triangle OQP with sides OM = 13 cm, MN = 5.5 cm, ON = 12 cm, NQ = 36 cm, and variables $x$ and $y$ representing lengths OP and

1. **State the problem:** We need to find the angle $\theta$ that the slide makes with the ground. The slide forms a right triangle where the height is 107 cm and the hypotenuse (s

1. **Problem statement:** In the right triangle ABC with right angle at B, sides AB = 7 units and BC = 6 units, identify the acute angle at vertex C. 2. **Recall:** In a right tria

1. The problem asks to find the acute angles in a right triangle with vertices A, B, and C, where B is the right angle. 2. Given: side opposite B (hypotenuse) = 7, side opposite C

1. **Stating the problem:** We need to find the area of a kite-shaped quadrilateral with diagonals intersecting at right angles. The kite has sides 13, 13, 15, and 15, and one diag

1. The problem asks to construct a line segment congruent to the segment $\overline{GH}$.\n\n2. To solve this, we need to understand that two line segments are congruent if they ha

1. **Problem statement:** A plot of land has an area of 876 m² and is divided into three rectangular fields of equal width. The total fencing used is 177 m, which includes the peri

1. **Problem:** Find the perimeter of triangle \(\triangle MNP\) where sides are given as \(5x - 34\), \(25\), and \(22\), and angle at \(P\) is \(x + 4\). We need to find the peri

1. **Identify all pairs of parallel segments.** Given the parallelogram and segments:

1. **Problem statement:** Calculate the side length of the equilateral triangle inscribed in an isosceles right triangle with base $c=12.0$ cm as shown in Abb. 3.150 a).

1. **State the problem:** We have three identical rectangles arranged in an L shape on the coordinate plane. The bottom-left corner of the bottom-left rectangle is at point $(1,4)$

1. **Problem statement:** We have a quadrilateral subdivided into two triangles by a segment DE parallel to AB. Given lengths are $AB=8$, $DE=5$, and $BC=10$. We need to find the l

1. The problem states that segments AB and DE are parallel, and we have two triangles ABC and DCE with given side lengths. We need to find the length $x$ of segment CD. 2. Since AB

1. The problem asks for a degree of rotational symmetry of a regular pentagon. 2. A regular pentagon has 5 equal sides and 5 equal angles.

1. **State the problem:** We need to find the radius $r$ of a circle given its circumference $C = 69.08$ feet. 2. **Formula used:** The circumference of a circle is related to its

1. **State the problem:** We need to find the circumference $C$ of a circle with diameter $d = 15$ feet. 2. **Formula:** The circumference of a circle is given by the formula:

1. The problem asks us to determine if John and Miles beat or missed their goal of canoeing at least 14 miles based on the graph. 2. The path starts at point $(-7,-2)$ and ends at

1. **State the problem:** We need to find the scale factor used to transform rectangle X into rectangle Y and express it as a percentage to one decimal place. 2. **Identify given d

1. The problem asks to identify two words that describe each of the seven triangles based on their angles and side lengths. 2. Important definitions: