📐 geometry

1. **Stating the problem:** We have a sequence of T-shaped patterns made of square tiles each with side length 1 cm. - Pattern 1 has 5 tiles: a horizontal row of 3 tiles and a vert

1. Let's start by stating the problem: We want to understand the theorems related to isosceles and equilateral triangles. 2. **Isosceles Triangle Theorem:** This theorem states tha

1. **Stating the problem:** Construct triangle $\triangle ABC$ and draw its circumcircle for the given cases.

1. সমস্যাটি হলো: একটি সুষম ষড়ভুজের কেন্দ্র থেকে শীর্ষবিন্দুগুলোর কেন্দ্রস্থ কোণের মান নির্ণয় এবং ক্ষেত্রফল বের করা। 2. সুষম ষড়ভুজের প্রতিটি কেন্দ্রস্থ কোণের মান নির্ণয়ের সূত্র হল

1. **Problem statement:** We are given triangle $\triangle EFG$ with incenter $S$, where angle bisectors $ES$, $FS$, and $GS$ meet. Points $P$, $Q$, and $R$ are the feet of perpend

1. **State the problem:** We need to find the area of quadrilateral ABCD with sides AB = 7 cm, BC = 15 cm, CD = 25 cm, diagonal AC = 20 cm, and a right angle at vertex C. 2. **Anal

1. **Stating the problem:** We have a scale drawing where 1 cm represents 100 km.

1. **Problem Statement:** Calculate the cost to fill a cylindrical water drum with radius 0.3 m and height 1 m, given water costs 50 per cubic meter. 2. **Formula:** The volume $V$

1. **Problem Statement:** Find the angle between the diagonal $AG$ and the plane $EFGH$.

1. **State the problem:** We need to find the values of angles $x$, $y$, and $z$ in the quadrilateral $ABCD$ where $\angle B = 121^\circ$, $\angle A = 40^\circ$, and $AB \parallel

1. **State the problem:** Find the area of the curved segment of a circle given the radius of curvature $R=100$ m and sagitta (height) $h=100$ m. 2. **Given data:**

1. **State the problem:** We need to find the area of the curved region (a segment of a circle) given the radius of curvature and the sagitta (height) of the arc. 2. **Given data:*

1. **Stating the problem:** We have two parallel lines \(m\) and \(a\) cut by two transversals \(r\) and \(v\). Given angles are \(5a\) near \(r\) and \(m\), \(85^\circ\) near \(r\

1. **Stating the problem:** We are given seven angles labeled $m\angle 1$ through $m\angle 7$ with specific degree measures. The problem involves understanding how these angle meas

1. **State the problem:** We have a parallelogram with an area of 40 units squared, a height of 5 units, and an unknown base $b$. We need to find the value of $b$. 2. **Formula for

1. **State the problem:** We have a right triangle with base length 4 units and height $x$ units. The area of the triangle is given as 16 units². We need to find the missing length

1. **State the problem:** Given two triangles $DEF$ and $GHI$ with right angles at $E$ and $H$ respectively, and the proportion $\frac{DE}{GH} = \frac{EF}{HI}$ along with $xE \cong

1. **State the problem:** Prove that $$\frac{EF}{HI} = \frac{DF}{GI}$$ given the proportions $$\frac{DE}{EF} = \frac{EF}{GH}$$ and $$\frac{GH}{HI} = \frac{HI}{DF}$$, and that $$\an

1. **State the problem:** Given that $\frac{JL}{NL} = \frac{KL}{ML}$ and $JL = ML$, prove that $\angle J \cong \angle N$. 2. **Analyze the given information:** We have two triangle

1. **State the problem:** Given triangles DEF and HGI with DE = EF, GH = HI, and \(\angle E \cong \angle H\), prove that EF = DF and HI = GI.

1. **State the problem:** Prove that $\angle E \cong \angle H$ given the similarity of triangles $\triangle DEF \sim \triangle GHI$ and the ratio $\frac{DE}{GH} = \frac{DF}{GI} = E