📐 geometry

1. The problem involves finding the values of angles $a$ and $b$ in a circle with points $P, Q, R, T$ on the circumference and given angle measures. 2. Given $m\angle PQT = 180^\ci

1. **State the problem:** We have two congruent trapezoids ABCD and JKLM. Given angles and side lengths in ABCD, find the measure of angle $\angle L$ and the length $JK$ in trapezo

1. **State the problem:** We have two congruent trapezoids ABCD and JKLM. Given some side lengths and angles in ABCD, we need to find the measure of angle $\angle L$ and the length

1. נניח שהבעיה היא למצוא את הערכים של הקטעים EF ו-MN. 2. לפי הנתונים, EF שווה 18 ו-MN שווה 14.

1. **הבעיה:** נתון טרפז ABCD עם בסיסים AB ו-DC, וקטעים EF ו-MN מקבילים לבסיסים. נתונים: $AB=BC=12$ ס"מ, $DC=24$ ס"מ, $AD=18$ ס"מ, $AM=3$ ס"מ, $CF=6$ ס"מ. יש לחשב את אורכי הקטעים EF

1. **Stating the problem:** We will cover the key concepts of the Circle topic for class 10, including definitions, formulas, and example questions similar to previous year board e

1. **Stating the problem:** Quadrilateral ABCD is similar to quadrilateral PQRS. We need to find: (a) The ratio of the length of AB to the length of PQ in the form $1:n$.

1. نبدأ بحل السؤال الأول: إذا كانت الأطوال مقدرة بالسنتيمتر، المطلوب حساب $س + ص$ في الشكل المعطى. 2. بالنظر إلى الشكل، نلاحظ أن هناك علاقات بين الأطوال المعطاة:

1. **Problem Statement:** In the given figure, if $PU = ST$ and $PQ = RS$, prove that $\angle PQU = \angle TRS$. 2. **Given:**

1. **Problem statement:** Given points P(2,9), T(10,-3), R(n,-13), and M as the midpoint of PT in parallelogram PARM, find: 3.1.1 Length of PT

1. **Problem statement:** We are given a triangle with vertices A, B, C, and D, where angle B is 128° and line CD forms approximately an 80° angle with the horizontal line AD. We n

1. **Problem Statement:** Given a cyclic quadrilateral ABCD inscribed in a circle, with triangle ABD isosceles where AD = BD, and angle ABC = 110°. 2. **Goal:** Find the values of

1. **Problem Statement:** We are given a triangle BCD with angle B measuring 128° and points B, C, D positioned on a semicircular protractor. We need to find the size of angle BCD

1. **Problem statement:** We are given a protractor image with points A, B, C, and D. Angle ABC is 128° and segment AD is a straight horizontal line along the 0°-180° base of the p

1. **State the problem:** We have a triangle with three angles labeled $a$, $a - 31^\circ$, and $a - 43^\circ$. We need to find the value of $a$. 2. **Recall the triangle angle sum

1. **Nyatakan masalah:** Diberi sektor AOB dengan pusat O, sudut tirus $\theta$ radian, panjang jejari $j$ cm, perimeter sektor 12 cm, dan luas sektor 5 cm². 2. **Formula penting:*

1. **Problem statement:** Given triangle ABC with vertices A(-3,7), B(-8,2), and C(4,6), and point D(-2,k) as the midpoint of BC, we need to: 3.1 Determine the gradient of BC.

1. نبدأ ببيان المسألة: لدينا مثلث ABC بأضلاع $AC=6$ سم، $AB=7$ سم، و$BC=5$ سم. 2. النقطة E هي نقطة على المستقيم AB بالنسبة للنقطة B، والنقطة F هي نقطة على المستقيم AC بالنسبة للنقط

1. **Problem Statement:** Find the value of $x$ in the circle with center $O$ where an angle of $35^\circ$ and an unknown angle $x^\circ$ are given on the circumference.

1. **Problem statement:** In triangle ABC, point D lies on segment AC such that |AD| = |DC|. Given \(\angle DBC = 15^\circ\) and \(\angle ACB = 30^\circ\), find \(\angle ABC\). 2.

1. **Problem statement:** Find the value of $x$ in the first figure where a triangle inside a circle with center $O$ has angles $30^\circ$, $70^\circ$, and $x^\circ$. 2. **Formula