📐 geometry

1. **Énoncé du problème :** On considère un triangle ABC avec I milieu de [AB] et J milieu de [AC].

1. The problem asks to find the scale factor for the transformation of points. 2. The scale factor is found by dividing the coordinates of the image point by the corresponding coor

1. **Problem Statement:** Pentagon EFGHI is rotated 180° clockwise about point I to form pentagon E'F'G'H'I'. We need to determine which line segment is parallel to TH'.

1. **Problem Statement:** Given a circle ABCDEF with center O, tangents TA and TE, and lines BGF and COT. We know CT is parallel to BA and \(\angle OTE = 32^\circ\). We need to fin

1. **Problem Statement:** Find the volume of the solid shape composed of a square prism and a triangular pyramid on top. 2. **Given:**

1. **Problem Statement:** Find the area of triangle ABC with vertices \(A(18, -2, -12)\), \(B(14, 4, -10)\), and \(C(7, 6, -6)\). 2. **Formula:** The area of a triangle given by po

1. **Problem Statement:** We have a diagonal line crossing through 12 congruent squares arranged in two offset rows, forming a stepped shape. We need to find the value of $\cos(x)$

1. **Problem Statement:** We have a triangle with vertices A(2,6), B(2,3), and C(4,4). We want to find the coordinates of the images after reflecting the triangle first in the x-ax

1. **State the problem:** Find the midpoint of the line segment with endpoint A at coordinates $(2,3)$. Since only one endpoint is given, we need the other endpoint to find the mid

1. **Problem Statement:** A ladder makes an angle of 60° with the ground, and the foot of the ladder is 8 m away from the wall. Find the length of the ladder. 2. **Formula Used:**

1. **Problem statement:** We have two secant segments \(\overline{IT}\) and \(\overline{MT}\) intersecting outside a circle at point \(T\). Points \(H\) and \(U\) lie on the circle

1. **Problem Statement:** We have an isosceles trapezium PQRS with lines TU, PQ, and SR parallel. Given the ratio $ST : TP = 3 : 4$ and the length $RQ = 42$ cm, we need to find the

1. **State the problem:** Find the volume of a cylinder with radius $r=8$ units and height $h=6$ units. 2. **Formula:** The volume $V$ of a cylinder is given by the formula:

1. **State the problem:** Hong wants to paint the ceiling of his restaurant, which is a square with side length 55 feet. Each can of paint covers 275 square feet. We need to find h

1. **State the problem:** Christine needs to stain a rectangular court floor with length 46 feet and width 35 feet. Each can of stain covers 115 square feet. We need to find how ma

1. **State the problem:** We need to find the area of the part of Jenny's garden that has carrots. The garden is divided into rectangular sections with given dimensions. 2. **Under

1. **Problem Statement:** Identify the shape of the cross section formed when a plane passes through each given solid.

1. **Problem statement:** We are given an isosceles triangle CDE with two equal angles at D and E, one angle at C is $34^\circ$, and the third angle is given as $(8x - 23)^\circ$.

1. **Problem statement:** We have a crane with a vertical tower 22 m tall and a horizontal arm 44 m long. A support cable forms a right triangle with vertical segment 24 m and hori

1. The problem asks to identify which pairs of angles are alternate interior angles given two parallel lines \(\overline{EG}\) and \(\overline{HJ}\) cut by a transversal line \(KFD

1. **Stating the problem:** Find the values of $x$ and $y$ in the given polygon where some interior and exterior angles are labeled, including an interior angle of $130^\circ$, an