📐 geometry

1. समस्या को समझें: त्रिभुज ABC में, P एक समद्विभाजक बिंदु है जो कोण B और कोण C को विभाजित करता है। दिया गया है कि BC ∥ LM और LM = BL + CM है। हमें यह सिद्ध करना है कि BC ∥ LM। 2.

1. The problem states that RS is the diameter of a circle with center O, and we need to find the value of angle $y$ at point S on the circumference. 2. Important fact: The angle su

1. **State the problem:** We need to find the area of the shaded shape WXZY, which is the area between two circular sectors OWX and OYZ with the same central angle of 75° but diffe

1. **State the problem:** We have a sector OAB of a circle with radius $r = 5.9$ mm and area $28$ mm². We need to find the central angle $\theta$ in degrees to 1 decimal place. 2.

1. **Problem 12:** Given $m\angle ABC = 35^\circ$, $m\angle BAC = 29^\circ$, and $\angle ACB \cong \angle DEB$, find $m\angle DEB$. 2. Since $\triangle ABC$ is a triangle, the sum

1. **State the problem:** We are given two triangles ABC and DEF with some angles and side lengths. We need to determine if they are similar and, if possible, find the unknown side

1. **Stating the problem:** We are given two triangles, ABC and DEF, with angles $A=63^\circ$, $B=48^\circ$, $E=89^\circ$, and $F=48^\circ$. We want to find the missing angles $C$

1. **Problem statement:** Given that triangles \(\triangle CDE\) and \(\triangle FCE\) are similar (\(\triangle CDE \sim \triangle FCE\)), find the value of \(x\) where \(CE = x\).

1. **Problem:** Find the scale factor of Figure B to Figure A given sides of triangles. Given sides:

1. **Problem Statement:** We need to find the image of triangle $\triangle KLM$ after reflecting it over the line $x = -1$. 2. **Given:**

1. **State the problem:** We have a translation transformation $T$ that maps point $P(-2, 2)$ to $P'(0, 0)$. We need to find the image of the point $(5, -1)$ under the same transla

1. Use the Pythagorean theorem to find the unknown sides. **Problem:**

1. **Problem Statement:** Find the length $d$ of the base of the large right triangle given the height is 12 m, one angle is 35°, and there is a smaller triangle inside with a 10°

1. **Problem Statement:** Given a cube with edges of length 6 cm, find:

1. **State the problem:** Find the area of the irregular polygon with given side lengths in miles. 2. **Approach:** We can divide the irregular polygon into simpler rectangles and

1. The problem is to find the area of an irregular polygon composed of a triangle and a stepped rectangular shape. 2. The triangle has a base of 8 km and height of 9 km. The area o

1. **Stating the problem:** We are given a triangle ABC with point D on BC such that \(\overrightarrow{BD}\) bisects \(\angle ABC\) which measures 40°. 2. The angle bisector divide

1. **Problem Statement:** We are given a quadrilateral with points A, B, C, D, E, F such that AD = DB and AF = FC. The lengths DF = 14 and DE = 10 are known. We need to find the le

1. **Problem Statement:** We have triangle ABC with points D, E, and F on its sides. Given that AE = EC and BF = FC, points E and F are midpoints of sides AC and BC respectively. W

1. **Problem Statement:** Given triangle ABC with points D, E, and F on the sides such that AD = DB, AE = EC, EF = 6, and $m\angle AED = 32^\circ$. We need to find $m\angle ECF$. 2

1. **Problem Statement:** We are given triangle $ABC$ with $AE = EC$, $m\angle BAC = m\angle DFE$, $AC = 24$, and $m\angle DFE = 126^\circ$. We need to find the length of segment $