📐 geometry

1. **Problem Statement:** Identify which pairs of angles are congruent among the given options: \(\angle 7 \text{ and } \angle 4\), \(\angle 6 \text{ and } \angle 8\), \(\angle 8 \

1. The problem is to find the angle \(\theta\) given some information about a triangle or vectors, often referred to as "angle fida" in some contexts. 2. To find an angle in a tria

1. **הבעיה:** במשולש ABC, חוצה הזווית החיצונית שליד זווית B וחוצה הזווית החיצונית שליד זווית C נפגשים בנקודה O. יש להוכיח כי AO הוא חוצה הזווית A. 2. **הגדרות וכללים חשובים:**

1. **הבעיה:** במשולש ישר זווית ABC עם זווית ישרה ב-B, AD הוא חוצה זווית של הזווית A. יש להוכיח כי $BD < DC$. 2. **נתונים:**

1. **State the problem:** We have a cylindrical tank with diameter 12 ft and height 2.5 m. We need to find:

1. **Stating the problem:** We have a frame with dimensions 16×2 on the top side and 6×12×1.5 on the right side, resembling a square-like frame with notches. We want to understand

1. **State the problem:** We need to find the value of angle $x$ in a figure where there is a triangle adjacent to a straight line segment with an angle of 120 degrees at point $R$

1. **State the problem:** We have two concentric semicircles with inner radius $r=6$ cm and outer radius $R=15$ cm, and a total horizontal length of 216 cm. We need to find the vol

1. **State the problem:** We have trapezoid ABCD with AB parallel to CD, AB = 12 cm, CD = 18 cm, and \(\angle B = 124^\circ\). Points E and F lie on AD and BC respectively, with EF

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