📐 geometry

1. **Problem statement:** Given the geometric figure with triangles and angles, we need to find:

1. **Problem Statement:** Given two pairs of parallel lines $l \parallel m$ and $p \parallel q$, find the values of angles $x$, $y$, and $z$ based on the given angles in the figure

1. **State the problem:** We need to find the volume of a triangular prism with a base triangle of base length 8 inches and height 4 inches, and the prism length (depth) is 10 inch

1. **State the problem:** Find the volume of a rectangular pyramid with base length 12 inches, base width 10 inches, and height 8 inches. 2. **Formula:** The volume $V$ of a pyrami

1. **Stating the problem:** We have a right triangle $\triangle ABC$ with right angle at $A$. The base $CA = 5.8$ cm and the height $AB = 4.5$ cm. Point $H$ lies on the hypotenuse

1. **State the problem:** We have two rectangles, one inside the other. The outer rectangle has width 6 units and height 11 units. The inner rectangle is centered inside the outer

1. **State the problem:** We have an isosceles right triangle XYZ with points Z(2, 3) and X(5, 3). The right angle is at X. We need to find the coordinates of vertex Y. 2. **Unders

1. **State the problem:** Find the area of triangle $\triangle ABC$ where sides $AB = BC = 40$ m and base $AC = 50$ m. 2. **Formula used:** The area of a triangle can be found usin

1. The problem involves calculating perimeters or circumferences based on given dimensions. 2. The formulas for each shape are:

1. **State the problem:** Calculate the circle's circumference, the square's perimeter, and the parallelogram's perimeter given:

1. **Énoncé du problème :** Nous avons la droite $\mathcal{D}$ d'équation $3x + 4y - 8 = 0$ et un point $A(2;3)$. Nous voulons écrire une fonction Python qui teste si un point $M(x

1. The problem is to find the measure of the missing angle in a triangle where the other two angles are given as 76° and 56°. 2. The formula used is the Triangle Angle Sum Theorem,

1. The problem is to find the measure of the missing angle in a triangle where the other two angles are given as 149° and 87°. 2. The formula used is the Triangle Angle Sum Theorem

1. The problem asks to identify the name given to the repeating pattern formed by the shapes shown in the diagram. 2. The diagram shows a sequence of interconnected rhombus shapes

1. **State the problem:** We have a trapezoid with the top base labeled as $-4w + 46$, the bottom base as $22$, and the two non-parallel sides marked equal, meaning the trapezoid i

1. **State the problem:** We have a circle defined by the equation $$x^2 + y^2 = 25$$. 2. **Find the centre and radius:** The general form of a circle equation is $$ (x - h)^2 + (y

1. **State the problem:** We have two parallel lines $m$ and $n$ cut by a transversal. The angles given are $(9x - 13)^\circ$ on line $m$, $(3x - 11)^\circ$ on line $n$, and an adj

1. **State the problem:** We have two parallel lines $m$ and $n$ cut by a transversal, creating angles labeled as $(9x+2)^\circ$, $(5x-18)^\circ$ near line $m$, and $(2y+20)^\circ$

1. مسئله: در شکل داده شده، باید حداقل چند چوب کبریت حذف کنیم تا دقیقاً سه مثلث در شکل باقی بماند، بدون اینکه چوب کبریتی اضافه بماند. 2. توضیح: هر مثلث از سه ضلع تشکیل شده است. حذف

1. **Stating the problem:** Find the measure of the angle marked with a letter in diagram 2(e), where angles 91° and 36° are given in a figure with points A, B, C, D, E.

1. Problem 26: Given a right triangle with hypotenuse 9, legs $x$ and $y$, find $x$ and $y$. 2. Use the Pythagorean theorem: $$x^2 + y^2 = 9^2 = 81$$