📐 geometry

1. مسئله: قرینه نقطه $A(3,9)$ نسبت به خط $y=2x+3$ داده شده است و نقطه قرینه $A'(b,4)$ است. هدف یافتن مقدار $ab$ است. 2. فرمول و توضیح: برای یافتن قرینه یک نقطه نسبت به یک خط، ابتدا

1. مسئله: قرینه نقطه $A(3,2)$ نسبت به خط $3x + y = 27$ را پیدا کنیم و مقدار حاصل‌ضرب $a$ و $b$ را بیابیم که نقطه قرینه $A'(b,4)$ است. 2. فرمول و توضیح: قرینه یک نقطه نسبت به یک خط،

1. مسئله: قرینه نقطه $A(1,2)$ نسبت به خط $y=2x+3$ نقطه $A'(b,4)$ است. مقدار $ab$ را بیابید. 2. فرمول و توضیح: برای یافتن قرینه یک نقطه نسبت به یک خط، ابتدا باید معادله خط را به فرم

1. مسئله: قرینه نقطه $A(3,2)$ نسبت به خط $y=2x+3$ نقطه $A'(b,4)$ است. باید مقدار $ab$ را پیدا کنیم. 2. فرمول و توضیح: برای یافتن قرینه یک نقطه نسبت به یک خط، ابتدا باید معادله خط ر

1. مسئله: نقطه A(3,1) نسبت به خط ۳x + ۲y = ۷ قرینه شده و نقطه قرینه A'(b,4) است. باید مقدار حاصل‌ضرب ab را پیدا کنیم. 2. فرمول قرینه نسبت به خط: اگر نقطه‌ای P(x_0,y_0) نسبت به خط A

1. **Problem Statement:** We are given a circle with center $O$ and a tangent line $AC$ touching the circle at point $C$. We need to find the measure of angle $\angle OAC$, which i

1. The problem is to understand the notation \overleftrightarrow{AC}, which represents a line passing through points A and C. 2. In geometry, the notation \overleftrightarrow{AC} m

1. **Problem Statement:** Given rectangle JKLM with points J (top-left), K (top-right), L (bottom-right), and M (bottom-left), and a diagonal JL drawn.

1. **Problem Statement:** Find the measures of angles $M$ and $K$ given the geometric figure or context (not provided explicitly). 2. **Assumptions and Formula:** Typically, angles

1. Let's clarify the RHS (Right angle-Hypotenuse-Side) theorem. It states that if two right-angled triangles have their hypotenuse and one corresponding side equal, then the triang

1. **Problem Statement:** Given rectangle JKLM with vertices J (top-left), K (top-right), L (bottom-right), and M (bottom-left), and a diagonal JL drawn.

1. **State the problem:** We need to find the area of the floor of the shed, which is represented by a polygon with vertices at approximately (20,20), (20,80), (50,60), and (50,20)

1. Let's understand the problem: We need to find the perimeter and area of regular figures, volume and surface area of solids, and area of irregular figures using mathematical meth

1. **State the problem:** We need to find the total area of a composite figure made of two parts: a rectangle on top and a trapezoid below. 2. **Identify the shapes and their dimen

1. **Problem statement:** Find the missing angles \(\angle 1\) and \(\angle 2\) in each figure and provide a reason for the answer. ### Part a)

1. Problem 3: Find the volume of the bottle crate, a rectangular prism with dimensions 90 cm (length), 60 cm (width), and 80 cm (height). 2. Volume of a rectangular prism is given

1. **Shape a**: Two quarter circles joined at a right angle, height 28 cm. - Each quarter circle radius $r=28$ cm.

1. ප්‍රශ්නය: වෘත්තයක් සම්බන්ධ ගැටලු විසඳීම. 2. වෘත්තයක් යනු, මධ්‍යස්ථානයක සිට සෑම ලක්ෂ්‍යයක් දක්වා දුර සමාන වන ලක්ෂ්‍යයන්ගේ සමුහයකි.

1. **Stating the problem:** We will explain the concept of geometric construction and solve an example: constructing the perpendicular bisector of a line segment. 2. **What is geom

1. **State the problem:** We have two right triangles. The smaller triangle has legs 14 and 8 units. The larger triangle has legs 21 and 12 units, and a hypotenuse of 24 units. We

1. **State the problem:** We have two right triangles. The first triangle has legs 14 and 8 units. The second triangle has legs 21 and 12 units, and the hypotenuse is labeled 24 un