📐 geometry

1. **Problem statement:** Given triangle ABC with points M on BC, X on AB, Z on AC such that XZ is parallel to BC. Given lengths: AZ = 3 cm, ZC = 2 cm, BM = 3 cm, MC = 5 cm. Find t

1. **Problem Statement:** Find the angle $\angle ADC$ given that $\angle ADB = \angle CDB$ (equal chords subtend equal angles at the circumference) and the circle touches quadrilat

1. **Problem Statement:** We have a parallelogram ABCD with diagonal BD intersecting line segment AE at point F, where E is any point on side BC. We need to prove that $$\frac{DF}{

1. **State the problem:** Given that segment $XM$ bisects segment $AO$ and angle $X$ equals angle $M$, prove that triangles $AXI$ and $OMI$ are congruent. 2. **Identify given infor

1. The problem asks to identify a solid with surfaces that are fully or partially curved. 2. In geometry, solids can have flat surfaces (like cubes) or curved surfaces (like sphere

1. The problem asks: What is a shape with all sides or maximum sides curved called? 2. In geometry, shapes can have straight or curved sides. When a shape has all sides curved, it

1. The problem asks to classify the given quadrilaterals based on their properties. 2. The first figure is a square with two diagonals intersecting at the center. A square is a qua

1. **Problem:** Find the surface area of the L-shaped prism with edges 12 yd, 11 yd vertically, 3 yd along top, and two 4 yd segments horizontally. 2. **Formula:** Surface area of

1. The problem asks to find the surface area of each solid figure shown. 2. The surface area of a solid figure is the total area of all its outer surfaces.

1. **Stating the problem:** Given a circle with center O, radius AO = 21 cm, and central angle \(\angle AOB = 60^\circ\), we want to analyze the properties of segments and arcs rel

1. **State the problem:** We have an isosceles triangle with one angle given as 104° and the two base angles equal, one labeled as $92 - 2x$ degrees. We need to find the value of $

1. **State the problem:** We are given that ray RT bisects angle \(\angle QRS\), meaning it divides \(\angle QRS\) into two equal angles. The measure of \(\angle QRS\) is 122 degre

1. The problem asks for the translation rule that maps segment BC to B'C'. 2. Given points:

1. **Problem statement:** Determine $X$ and $Z$ such that points $A(-1,0,3)$, $B(3,-2,6)$, and $C(X,2,Z)$ are collinear. 2. **Formula and rule:** Three points are collinear if the

1. **State the problem:** We need to find the image of trapezoid JKLM after reflecting it over the vertical line $x = -1$. 2. **Reflection formula:** When reflecting a point $(x,y)

1. The problem asks to construct the graphs of the functions related to the triangle with vertices at (0,0), (20,0), and (20,5). 2. The triangle has three sides: the horizontal sid

1. **Problem Statement:** Find the coordinates of points B and D on the computer screen window, and calculate distances from A to C and B to D given pixel size. Also, identify whic

1. **Problem:** Draw a triangle with inradius 3 cm and two angles 50° and 70°. 2. **Formula and rules:**

1. The problem is to find the sum of the rhombus, which typically means finding the sum of its diagonals or perimeter depending on context. Here, we clarify the sum of the diagonal

1. **State the problem:** We need to solve for the height $h$ of a cylindrical can given its volume $V = 1188$ cubic inches and the formula for the volume of a cylinder:

1. **Nêu bài toán:** Cho tam giác $\triangle ABC$ với $AB < AC$. Kẻ tia phân giác $AD$ của góc $BAC$ với $D \in BC$. Trên cạnh $AC$ lấy điểm $E$ sao cho $AE = AB$, trên tia $AB$ lấ