📐 geometry

1. **State the problem:** We need to find the measures of angles 1, 2, 3, and 4 in a right triangle where angle 2 is given as 35° and the right angle is at the bottom left corner.

1. **Stating the problem:** We are given four angles around two intersecting lines forming a triangle with one right angle. The measures are $m\angle 1 = 35^\circ$, $m\angle 2 = 55

1. مسئله را بیان می‌کنیم: در یک مثلث متساوی الساقین، می‌خواهیم مجموع فاصله‌های هر نقطه روی قاعده از دو ساق را پیدا کنیم. 2. تعریف مثلث متساوی الساقین: مثلثی است که دو ضلع آن (دو سا

1. مسئله: مقدار $b$ را در راستای $x$ و $y$ پیدا کنید. 2. فرمول‌ها و قوانین مهم:

1. The problem states that triangle ABC is a right triangle with angle A = 90°. 2. A conjecture about right triangles might be something like "The hypotenuse is always the longest

1. **Problem statement:** We are given a quadrilateral ABGD with AD parallel to BC. The angles at points G, D, and C are 60°, 70°, and 60° respectively, and we need to find the val

1. **Problem Statement:** We have two parallel lines $x \parallel y$ and a transversal intersecting them, creating angles $a^\circ$, $b^\circ$, and $c^\circ$. We need to find the v

1. **Problem Statement:** We are given two parallel lines $l$ and $m$ intersected by a transversal, forming eight angles. Angle 2 measures $(3x + 70)^\circ$ and angle 5 measures $(

1. **Problem statement:** We have an isosceles triangle $\triangle ABC$ with $AB = AC$ and $\angle A = 40^\circ$. Points $B$, $C$, and $D$ are collinear, and we want to find the me

1. **State the problem:** We have a parallelogram ABCD with angles at vertices A and D labeled as $(x + 40)^\circ$ and $(x - 40)^\circ$ respectively. We need to find the value of $

1. **State the problem:** We have a point $P(-2, 3)$ that is translated to $P'(-6, -4)$. We need to find the translation rule. 2. **Recall the translation rule:** A translation mov

1. The problem asks for the degree of rotational symmetry of a regular hexagon. 2. A regular hexagon has 6 equal sides and 6 equal angles.

1. **Problem statement:** Given that point C is the midpoint of segment MN, determine which of the following statements is FALSE: - CM = 2(MN)

1. **Problem statement:** Find the radius of a cone when the curved surface area (CSA) is 286 cm² and the ratio of the radius to the slant height is 7:13. 2. **Formula for curved s

1. **Problem Statement:** Given circle T with points P, Q, R, and S on the circumference, and \(\angle PTQ \cong \angle RTS\), find the length of chord \(PQ\).

1. **Problem Statement:** Given that angles PTQ and STR are vertical angles and congruent, we need to determine which chords in the circle are congruent. 2. **Key Concept:** Vertic

1. Bài toán: Chứng minh tam giác đã cho là tam giác cân khi chưa biết các cạnh bằng nhau. 2. Công thức và quy tắc quan trọng: Tam giác cân là tam giác có ít nhất hai cạnh bằng nhau

1. **Nêu bài toán:** Chứng minh tam giác cân là tam giác có hai cạnh bằng nhau. 2. **Công thức và định nghĩa:** Tam giác cân là tam giác có hai cạnh bằng nhau, tức là nếu tam giác

1. **Problem Statement:** Calculate the volume of a warehouse shaped as a rectangular prism with dimensions length = 31 ft, width = 25 ft, and height = 30 ft. 2. **Formula:** The v

1. **Problem Statement:** Find the area of the shaded sector of a circle with radius $8$ units and central angle $60^\circ$. 2. **Formula:** The area $A$ of a sector with radius $r

1. **Problem Statement:** Given a circle centered at the origin $O(0,0)$, with points $A(3,4)$ and $B$ on the circle, find the length of the chord $AB$.