📐 geometry

1. **Problem Statement:** We have a stack of 7 identical cubes arranged in a stepped form. We want to find the minimum number of additional cubes needed to complete this stack into

1. The problem involves finding the value of $X$ formed by the intersection of lines $CE$ and $DB$ in a triangle configuration. 2. According to the problem, $CE$ and $DB$ intersect

1. The problem involves a square with side length 4 cm and four quarter circles drawn inside it, each centered at a corner of the square. 2. We want to find the area of the shaded

1. **Problem statement:** We are given a circle with two chords intersecting inside it, forming four angles. One angle is 25°, another is 84°, and we need to find the unknown angle

1. **State the problem:** We are given a circle with center O and two intersecting chords creating angles $x$ and $y$ at the circumference. The central angle between the two points

1. **State the problem:** We need to find the value of $x$ given two angles in a triangle: one angle on the circle is $x + 50$ degrees and the angle at point $O$ inside the triangl

1. The problem is to create an image of stained glass using corresponding equations. 2. Stained glass patterns can be modeled using geometric shapes and trigonometric functions to

1. The problem is to create a stained glass art design using mathematical equations. 2. Stained glass art can be represented by geometric shapes and curves, each described by equat

1. **State the problem:** We need to find the value of angle $x$ in a triangle inscribed in a circle, where one angle is given as $22^\circ$ and the triangle is connected to the ce

1. The problem asks to find the value of $x$ in a circle with two intersecting chords forming angles $x+10$ and $146^\circ$. 2. When two chords intersect inside a circle, the oppos

1. **State the problem:** Given that D is the midpoint of AC, AE ≅ CF, AB ⟂ DE, and BC ⟂ DF, prove that ∠A ≅ ∠C. 2. **Given:**

1. **State the problem:** Given that \(\overline{AB} \cong \overline{BC}\) and \(\angle ABE \cong \angle CBD\), prove that \(\triangle BED\) is an isosceles triangle. 2. **Recall t

1. **Problem Statement:** Given parallelogram KLMJ with diagonals intersecting, the segments of the diagonals are given as: - Segment J to intersection: $3y - 5$

1. **State the problem:** Given a parallelogram WXYZ with sides labeled as follows:

1. **Problem statement:** We need to find the cost of cementing the inside walls and base of a cylindrical water tank with an internal radius of 2.5 m and depth 4 m, at a rate of 6

1. **Problem statement:** Given points $A(1, -3, 2)$, $B(2, 5, 3)$, and $C(4, -3, 5)$ in space $Oxyz$, verify if $I(3, 1, -4)$ is the midpoint of segment $BC$. 2. **Formula for mid

1. **Problem statement:** Given isosceles triangle $\triangle ABC$ with $AB = AC$. $M$ is the midpoint of $BC$. Prove: a) $\triangle ABM$ is the angle bisector of $\angle BAC$ and

1. **Problem statement:** We have a rectangular yard ABCD with sides AB = 5m and AD = 12m.

1. **Problem statement:** Given isosceles triangle $\triangle ABC$ with $AB = AC$. $M$ is the midpoint of $BC$. Prove: a) $AM$ is the angle bisector of $\angle BAC$ and $AM \perp B

1. **Problem statement:** Find the sum of the interior angles of a pentagon. 2. **Formula:** The sum of interior angles of a polygon with $n$ sides is given by:

1. **Đề bài:** Cho tam giác ABC vuông tại A. Gọi M là trung điểm của cạnh BC. Trên tia đối của tia AM lấy điểm E sao cho ME = MA. Chứng minh: a) Tam giác AMB = tam giác EMC