📐 geometry

1. **Stating the problem:** We are given dimensions of a rectangular prism (balok) and a cube (kubus) and need to compare their volumes.

1. The problem asks to identify pairs of angles formed by two parallel lines $g$ and $h$ cut by a transversal $t$ that have equal measures. 2. When two parallel lines are cut by a

1. **Problem statement:** We need to find the length of the diagonal path of a rectangular area with length 18m and width 12m. 2. **Formula used:** The diagonal $d$ of a rectangle

1. **Problem 1: Composite solid with cylinder and hemispheres** We have a right circular cylinder with radius $r=4$ in and height $h=12$ in, capped by two hemispheres each of radiu

1. Problem: Find the images of points under given dilations. 2. Formula for dilation of a point $Q(x,y)$ about center $P(x_p,y_p)$ with scale factor $k$ is:

1. **State the problem:** Calculate the length of the diagonal path of a rectangular area with length 18m and width 12m, expressing the answer in surd form. 2. **Recall the formula

1. **State the problem:** Find the surface area of a cone with diameter 8 cm and slant height 13.6 cm. 2. **Formula:** The surface area $A$ of a cone is given by

1. **Problem statement:** Find the surface area of a cone with a base diameter of 8 cm and a slant height of 13.6 cm. 2. **Formula:** The surface area $A$ of a cone is given by

1. **Problem statement:** We have a regular pentagon ALLINE and a point R inside it such that triangle ARE is equilateral. We need to determine if points L, R, N are colinear.

1. **State the problem:** We have three congruent rectangles arranged so that each is rotated 90° around a vertex of the previous one. Given points $A(2,5)$ and $B(4,1.5)$, find co

1. **State the problem:** We have three line segments originating from a single point forming two angles: one angle is $(3z+2)^\circ$ and the other is $(8z)^\circ$. There is a righ

1. **State the problem:** We are given two angles formed by intersecting lines, labeled as $(2a+3)^\circ$ and $(6a+1)^\circ$. We need to find the value of $a$. 2. **Identify the re

1. **State the problem:** We have a triangle \(\triangle DEF\) with vertices \(D(1,6)\), \(E(2,-5)\), and \(F(-4,-2)\). A dilation centered at the origin with scale factor 2 is app

1. **State the problem:** We need to prove that triangles $\triangle GHJ$ and $\triangle GKJ$ are congruent given that $GH \perp HJ$, $GK \perp KJ$, and $GH = GK$. 2. **Identify th

1. **Problem Statement:** Given triangle points A, B, C, and D with BC \cong DC and \(m\angle ACB > m\angle ACD\), determine the relationship between segments AB and AD. 2. **Key I

1. **State the problem:** We have a right triangle with hypotenuse length 17 cm. The height is 7 cm longer than the base. We need to find the base and height. 2. **Set variables:**

1. **Problem statement:** We have a trapezoid with two diagonals intersecting inside it, forming an angle $x$ at the intersection. Two angles near the intersection are given: $38^\

1. **State the problem:** Stephanie puts 30 cubes in a box. Each cube is $\frac{1}{2}$ inch on each side. The box holds 2 layers with 15 cubes in each layer. We need to find the vo

1. **State the problem:** We need to find the values of $x$ and $y$ in the given circle diagrams and the length of line segment $CE$. 2. **Analyze the first diagram:** The angle at

1. The problem asks which of the given angles could be the size of an exterior angle of a regular polygon. 2. The formula for the exterior angle $E$ of a regular polygon with $n$ s

1. The problem states that \(\angle 1\) and \(\angle 2\) are vertical angles, and their measures are given as \(m\angle 1 = (7x - 9)^\circ\) and \(m\angle 2 = (6x + 11)^\circ\). We