📐 geometry

1. **State the problem:** Find the distance between the points $(0,4)$ and $(5,0)$ in the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and

1. The user mentioned "perpendicular nhi dia hai," which means "perpendicular is not given." 2. In geometry and algebra, when two lines are perpendicular, their slopes satisfy the

1. **State the problem:** Find the distance between the points $(2,5)$ and $(5,9)$.\n\n2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in the p

1. **State the problem:** Find the distance between the points $(2,3)$ and $(5,-5)$ in the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ an

1. **Problem statement:** We have a roof support made of four wooden lengths: AB, AC, BC, and MC. Given:

1. Նշված է, որ $AO = OC$ և $\angle 1 = \angle 2$. 2. $AO = OC$ նշանակում է, որ $O$ կետը հատվածի $AC$ մեջտեղում է, այսինքն $O$-ն միջնակետ է։

1. Դու խնդրում ես օգնություն երկրաչափության առաջադրանքներով։ 2. Խնդրում եմ, ներկայացրու կոնկրետ առաջադրանքը, որպեսզի կարողանամ օգնել։

1. **State the problem:** We have a triangle RST with sides labeled as follows: RS = $x$, RT = $x + 50$, ST = $3x + 146$. Points P and Q lie on sides RS and RT respectively, with s

1. **Stating the problem:** We have a triangle PQR with PR = QR (isosceles triangle) and a point T on the extension of side PQ. We want to find the lengths of segments RS, TQ, and

1. Сформулюємо задачу: знайти нормальний вектор та рівняння площини, заданої рівнянням $x + 2y + 2z = 4$. 2. Формула площини у векторній формі: $Ax + By + Cz = D$, де $(A, B, C)$ —

1. Problem 15 asks: In rectangle ABCD, diagonals AC and BD intersect at O. Given \(\angle CDB = 54^\circ\), find \(\angle OAB\). 2. Important properties:

1. The problem asks to complete the congruence statement for the triangles shown in the figure. 2. Given triangles are \(\triangle YXW\) and \(\triangle ?\) with shared vertex \(W\

1. The problem asks to complete the congruence statement for the triangles in the rectangle DEFG, where \(\triangle DEG \cong \triangle ???\). 2. Given the rectangle DEFG with vert

1. The problem states that triangles \(\triangle TJM \cong \triangle PHS\). This means all corresponding angles and sides are congruent. 2. Since \(\triangle TJM \cong \triangle PH

1. **State the problem:** Given that triangles $\triangle TJM$ and $\triangle PHS$ are congruent, complete the statements about their corresponding angles and sides. 2. **Recall th

1. **State the problem:** We have a point $A(-6,3)$ and a translation rule $(x,y) \to (x+5, y-9)$. We want to find the coordinates of the image point $A'$ after applying this trans

1. **State the problem:** We need to find the perimeter of an L-shaped polygon with given side lengths: top horizontal segment = 10 cm, right vertical segment = 12 cm, and bottom h

1. Problem: In rhombus WEST, diagonals WS and TE measure 24 cm and 10 cm respectively. Find the length of side WE. 2. Formula: In a rhombus, diagonals bisect each other at right an

1. Problem II.A: Given in circle OD, $m\angle TE = 40^\circ$, find the measure of each arc UL, TY, LE, UET. 2. Since $m\angle TE = 40^\circ$ is an inscribed angle, the arc it inter

1. Problem 8: Rohit has 6 wooden sticks of equal length and wants to join them to form a regular polygon. Find the internal angle between the sticks. Formula: The internal angle of

1. **Problem Statement:** Given a circle with chord BC and a point P on BC such that AB = AP, prove that CP = CQ.