📐 geometry

1. **Problem Statement:** We need to find the image of rectangle TUWV after a 180° counterclockwise rotation about the origin. 2. **Vertices of the original rectangle:**

1. **Problem Statement:** We are given a triangle SRT with angles at vertices R and T expressed as $(3x + 1)^\circ$ and $(2x + 2)^\circ$ respectively. The sides SR and ST are congr

1. The problem involves understanding four key topics in Grade 8 math: Geometry of Straight Lines, Geometry of 2D Shapes, The Theorem of Pythagoras, and Area and Perimeter of 2D Sh

1. **Problem Statement:** Identify which of the given arcs is a minor arc on the circle. 2. **Definition:** A minor arc is an arc of a circle that is smaller than a semicircle (les

1. **Problem Statement:** Identify which angle among \(\angle DOB\), \(\angle BAC\), \(\angle EAC\), and \(\angle ABE\) is a central angle in the given circle. 2. **Definition:** A

1. **Problem Statement:** Identify which angle among \(\angle DOB\), \(\angle BAC\), \(\angle EAC\), and \(\angle ABE\) is an inscribed angle in the given circle. 2. **Definition:*

1. The problem asks to identify which arc in the figure represents a semicircle. 2. A semicircle is an arc that represents exactly half of a circle, which means it subtends an angl

1. **Problem Statement:** We are given a circle with a chord of length 5, and a point outside the circle connected to the circle by two segments of lengths 4 and 3. We need to find

1. **Problem statement:** We have a right triangle with hypotenuse length 15 feet. One leg is 3 feet longer than the other leg. We need to find the lengths of the two legs. 2. **Fo

1. **Problem Statement:** Find the perimeter of trapezoid WXYZ with sides WX = 3 cm, XY = 2.5 cm, YZ = 6.5 cm, and WZ = 5.2 cm. 2. **Formula for Perimeter:** The perimeter $P$ of a

1. **State the problem:** Given triangle MTL with MT \cong LT and OT bisects \angle MTL, prove that OT \perp LM. 2. **Given information:**

1. The problem asks to identify which pair is C.P.C.T.C., which stands for Corresponding Parts of Congruent Triangles are Congruent. 2. C.P.C.T.C. applies when two triangles are pr

1. **Problem Statement:** Prove that the altitude $AD$ of triangle $ABC$ is smaller than sides $AB$ and $AC$. Given $\angle BAC = 60^\circ$, $AC = 5$ cm, and $AD$ is the altitude f

1. **Problem Statement:** Given trapezium ABCD with AD || BC, AB = AD, BD = BC, and angle Ĉ = 80°. We need to determine the unknown angles.

1. Задача: Найти площадь боковой поверхности правильной усеченной пирамиды с основаниями $4\sqrt{3}$ и $10\sqrt{3}$, при угле между апофемой и основанием $60^\circ$. 2. Формулы и о

1. **Problem Statement:** We have a pentagon inscribed in a circle with given angles 25°, 32°, and 80°, and two unknown angles labeled \(\alpha\) and \(b\). We need to find the val

1. **State the problem:** We are given a triangle with three angles: 31°, 35°, and an unknown angle $x$. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:*

1. **Stating the problem:** We have two triangles with angles given as follows: - First triangle angles: $(5x - y)^\circ$ and $(3x + y)^\circ$.

1. **Stating the problem:** We are given two triangles with angles expressed in terms of $x$ and $y$, and some numerical angles. We need to verify angle relationships and solve for

1. **Problem Statement:** We are given three sets of information involving variables $x$ and $y$ related to angles in triangles and equations.

1. **Problem statement:** We need to find the height of an equilateral triangle with side length 7.4 m. 2. **Formula:** For an equilateral triangle with side length $a$, the height