📐 geometry

1. **Problem statement:** Given lines AC and DE are parallel, and DC is perpendicular to both AC and DE. Segment BD has length $\frac{4}{3}$. We need to find the length of side DE.

1. **Stating the problem:** Given points A(2,2), B(4,0), and C(-2,0), find the area of triangle ABC. 2. **Formula used:** The area of a triangle with vertices at coordinates $(x_1,

1. **State the problem:** We need to find a series of transformations that map polygon ABCDE with vertices near (1,3), (1,2), (2,1), (3,1), (3,3) onto polygon A'B'C'D'E' with verti

1. **State the problem:** We need to find the area of a square given its vertices at approximately (1.5, 3), (2, 6), (5, 5), and (4, 2.5). 2. **Recall the formula for the area of a

1. **Problem statement:** Given kite ABCD with BN = 15 and AB = 17, find the length of diagonal BD. 2. **Understanding the kite properties:** In a kite, two pairs of adjacent sides

1. **Problem statement:** Given kite ABCD with BN = 15 and AB = 17, find the length of diagonal BD. 2. **Understanding the kite properties:** In kite ABCD, diagonals intersect at r

1. The problem asks to identify which shapes are nets of cubes from the given descriptions. 2. A net of a cube consists of 6 squares connected edge-to-edge in a pattern that can be

1. The problem asks to identify the type of angles formed by angle 4 and angle 5 in the given diagram with two parallel lines $m$ and $n$ cut by a transversal $p$. 2. Important rul

1. **State the problem:** Prove that \(\triangle GED \cong \triangle GFD\) given that both are right triangles and \(\overline{DE} \cong \overline{DF}\). 2. **Given:**

1. **Problem Statement:** We have two circle diagrams with angles labeled a, b, c, d, and given angles 34° and 15°. We need to find the values of these unknown angles using circle

1. **State the problem:** We have a right triangle with a base of length $\frac{5}{4}$ units, a height $h$, a hypotenuse of length $\frac{3}{4}$ units, and one side adjacent to $h$

1. The problem asks to write a proportion showing that the slope of segment JL in triangle JKL is equal to the slope of segment MP in triangle MNP, given that the triangles are sim

1. **Problem Statement:** We have a triangle with angles 30° and 60°, and the side opposite the 60° angle is given as $\sqrt{10}$. We need to find the length of side $x$, which is

1. **Problem statement:** We have triangle KLM with interior angles $\angle M = 50^\circ$, $\angle L = 48^\circ$, and $\angle K = 82^\circ$. Points N, O, and P are midpoints of the

1. **Problem:** Find the missing angle $x$ in a circle where the arc measures 110° and $x$ is the inscribed angle opposite the arc. 2. **Formula:** The inscribed angle theorem stat

1. **State the problem:** We are given the circumference of a circle as 36.5 cm and need to find its area. 2. **Recall the formulas:**

1. **State the problem:** We need to find the volume of a cylindrical tin with height $20$ cm and radius $8$ cm. 2. **Formula for the volume of a cylinder:** The volume $V$ of a cy

1. נניח כי משולש הפיצה המקורי הוא משולש ישר זווית עם בסיס $20$ ס"מ וגובה $16$ ס"מ. 2. שטח המשולש המקורי הוא לפי הנוסחה:

1. المشكلة: لدينا نقطة إحداثياتها $(-3,4)$ ونريد تحديد موقعها في نظام الإحداثيات الديكارتية. 2. نظام الإحداثيات الديكارتية مقسم إلى أربعة أرباع:

1. সমস্যাটি হলো: (7,17) বিন্দু থেকে (9,9) বিন্দু পর্যন্ত সরলরেখার দৈর্ঘ্য নির্ণয় করা। 2. সরলরেখার দৈর্ঘ্য নির্ণয়ের সূত্র হলো: $$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ যেখানে $(

1. **Problem statement:** Calculate the volume of a round wading pool with diameter 125 cm and height 30 cm. Then find the water height if the pool contains 200 liters. 2. **Formul