📐 geometry

1. The problem is to understand and solve questions related to volume and surface area from Class 9 Maths by RS Aggarwal. 2. Volume is the amount of space occupied by a 3D object,

1. **Énoncé du problème :** On considère un triangle ABC avec les points E, F, G, K définis par des barycentres et des relations vectorielles.

1. **State the problem:** We have a map scale of 1 : 120000, meaning 1 cm on the map represents 120000 cm in real life.

1. **Problem Statement:** Calculate the area of the shaded region swept out on a flat windscreen by a wiper. The sector has a central angle of 120° and radius lines of 4 cm and 16

1. Problem: Calculate the value of an unknown angle in a triangle where two angles are given. 2. Formula: The sum of angles in a triangle is always $$180^\circ$$.

1. **Problem:** Find the point of intersection between Route A passing through (2,5) and (8,17) and Route B passing through (3,20) and (9,2). 2. **Step 1: Find the equations of the

1. The problem asks to find the scale factor of the enlargement from shape A to shape B. 2. The scale factor is the ratio of any corresponding lengths in shape B to shape A.

1. The problem asks to describe the surface corresponding to the equation $x=0$. 2. The equation $x=0$ represents the plane where the $x$-coordinate is always zero.

1. **Stating the problem:** We have triangle ABC with sides $AB=4$ cm, $BC=6$ cm, and $AC=3.5$ cm. Points $E$ and $F$ are midpoints of sides $AB$ and $AC$ respectively.

1. **Plotting points A-H in 3D space:** - Points: A(0,0,2), B(0,2,0), C(2,0,0), D(2,3,0), E(3,2,4), F(-2,0,4), G(-1,-1,-1), H(2,1,-2).

1. **State the problem:** We need to find the scale factor of enlargement from the smaller shape to the larger shape in each case. 2. **Formula and rule:** The scale factor of enla

1. The problem states that the opposite angles of a parallelogram are given as $(2x - 3)^\circ$ and $(45 - x)^\circ$. We need to find the value of $x$. 2. Important property: Oppos

1. **State the problem:** We have three congruent rectangles arranged so that each is rotated 90° around a vertex of the previous rectangle. Given points A(2,5) and B(4,1.5), find

1. **Problem statement:** We have a quadrilateral OXPY with diagonals OX and PY intersecting at point T. Given:

1. **Stating the problem:** We are given a circle with center O and a central angle $\alpha = 288^\circ$. Points A, B, C, D, and H lie on the circumference, and angles $x$, $y$, an

1. **State the problem:** Calculate the area of the shaded region formed by a large quarter circle of radius 12, a smaller quarter circle of radius 5, and a right triangle with leg

1. The problem asks which of the given shapes (A, B, or C) has rotational symmetry. 2. Rotational symmetry means a shape looks the same after being rotated by some angle less than

1. **Problem Statement:** We have triangle ABC with angle $\angle A = 45^\circ$ and a segment marked as $2\alpha$ near base BC. Point W lies on BC. We want to solve for unknowns or

1. **Problem statement:** We have an equilateral triangle ABC, and side BC is extended to point E such that C is the midpoint of BE. We need to find the measures of angles $\angle

1. مسئله: پنجره‌ای داریم که شامل یک مستطیل به عرض $x$ و ارتفاع $y$ است و بالای آن یک مثلث متساوی الاضلاع با ضلع $x$ قرار دارد. محیط کل پنجره برابر 8 متر است. می‌خواهیم طول ضلع مثلث

1. مسئله را بیان می‌کنیم: مثلثی با رئوس A(-1,2)، B(3,0)، C(1,-2) داده شده است. الف) معادله میانه AM را بیابید.