📐 geometry

1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal $t$, find the value of $x$ when the angles $(5x - 8)^\circ$ and $(4x + 8)^\circ$ are given a

1. The problem asks to find the distance between the points $A(0,0)$ and $B(-5,-6)$ on the coordinate plane. 2. The distance formula between two points $A(x_1,y_1)$ and $B(x_2,y_2)

1. **State the problem:** We need to find the area of a circle with a diameter of 14 mm. 2. **Formula for the area of a circle:** The area $A$ is given by the formula

1. **Stating the problem:** Identify which letter labels correspond to a major arc, a minor sector, and a major segment based on the given circle diagrams. 2. **Definitions and for

1. **State the problem:** We are given a triangle with vertices A, B, and C, and we need to find the smallest angle to the nearest degree. 2. **Identify the shortest side:** The sm

1. **State the problem:** We need to find the value of the angle $j$ given two adjacent angles $49.5^\circ$ and $79.3^\circ$ that together with $j$ form a straight line. 2. **Recal

1. **Problem statement:** Given a figure where $QR = 15$ and $QS = 45$, find the length of $RS$. 2. **Understanding the problem:** Points $Q$, $R$, and $S$ are on a line or form a

1. **Stating the problem:** We have a cube with side length 10 cm. Point M is the midpoint of segment TS. A string runs from point P to point Q passing through M. We need to find t

1. **Problem statement:** Find the value of $r$ in the first figure where two parallel lines are intersected by a transversal, and the angles given are $50^\circ$, $110^\circ$, and

1. **State the problem:** We are given a kite PLAY with PA = 12 cm and LY = 6 cm. We need to find the area of kite PLAY.

1. **Problem statement:** We have a frustum formed by removing a small cone from a larger similar cone. The small cone has radius $6$ m and height $10$ m. The frustum height is $50

1. **State the problem:** We need to find the volume of the frustum of a rectangular-based pyramid. The frustum is formed by cutting the original pyramid horizontally. 2. **Given d

1. The problem involves using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. 2. The Pythagorean theorem formula is $$a^2 + b^2 = c^2$$ where $

1. **State the problem:** We need to find the length $x$ in a trapezoid where the top base is 9, the bottom base is 31, and the diagonal is 19. A perpendicular line $x$ is drawn fr

1. **Stating the problem:** We have triangle vertices at points $A(2,2)$, $B(8,2)$, and $C(5,5)$. We want to find the new coordinates after rotating the triangle $90^\circ$ anticlo

1. **State the problem:** We have a convex pentagon with interior angles measuring $2v$, $2v + 43^\circ$, $2v + 12^\circ$, $96^\circ$, and $v + 25^\circ$. We need to find the value

1. **State the problem:** We need to find the number of sides $n$ of a regular polygon given that each interior angle measures 140°. 2. **Formula for interior angle of a regular po

1. **State the problem:** We need to find the volume of one hemisphere of the Earth, which is roughly spherical with a diameter of 12,800 km. 2. **Formula used:** The volume of a s

1. **State the problem:** Find the distance between the points $(-4,8)$ and $(4,4)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given b

1. **Problem statement:** Find the volume of water in the cylinder with a metal ball bearing fully submerged inside it. 2. **Given:**

1. **Problem Statement:** Identify similar triangles in the given figures and solve for missing sides using right triangle similarity and geometric mean theorems. 2. **Similar Tria