📐 geometry

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 $AB$.

1. **Problem statement:** Given a right triangular prism with a cross-sectional area of 8.5 cm² and one side length of 30 cm, find the volume of the prism. 2. **Formula used:** The

1. **Problem statement:** Given a triangle with points A, B, C, D, E on one side such that $AB=BC=CD=DE$ and the segment $BI=2$ cm. We need to find the length of $EF$. 2. **Underst

1. **Problem statement:** Given a circle with center $O$ and a triangle $PQR$ inside it, where $\angle QPR = 70^\circ$. We need to find the values of angles $x$ and $y$ marked at $

1. பிரச்சினையை விளக்குக: ஒரு 7 செ.மீ. ஆரையுடைய அரைவட்டத்தின் வில்லின் நீளத்தை காண வேண்டும். 2. அரைவட்டத்தின் வில்லின் நீளம் என்பது அரை வட்டத்தின் நேர்கோட்டின் நீளம் ஆகும், இது வட்ட

1. கொடுக்கப்பட்டுள்ள பிரிஸத்தின் குறுக்கு வெட்டு முகப்பரப்பளவு $8.5$ செ.மீ² ஆகும். 2. குறுக்கு வெட்டு என்பது அடிப்பகுதியில் உள்ள மூன்று கோணத்தின் பரப்பளவு ஆகும்.

1. **State the problem:** We are given a triangle with interior angles 40° and 80°, and an exterior angle adjacent to the triangle labeled $x^\circ$. We need to find the value of $